A big factor in their deliberations: Connecticut's estate and gift taxes, which tax assets above $2 million per individual at rates as high as 12%. Mr. Negele says some snowbirds at his Stamford retirement home have shifted their tax home to Florida, while others he knows have left the state altogether. Mr. Negele is far from alone, estate planners say. "State death taxes are considerably more important than they used to be, and we spend a lot of time planning for them," says Beth Kaufman, an estate-tax lawyer at Caplin & Drysdale in Washington, in part because of changes in the federal tax laws.
Nineteen states and the District of Columbia, home to just over one-third of the U.S. population, levy an estate tax on the assets of people who die or an inheritance tax on heirs receiving assets. Maryland and New Jersey have both, although each allows offsets to prevent double taxation.
In January, Congress voted to keep Uncle Sam's inflation-adjusted estate exemption above $5 million per individual ($10 million per married couple). The change excluded almost all Americans from the federal levy, so state-level taxes loom larger by contrast. (This year, the federal exemption is $5.25 million.)
Many states also have far smaller exemptions than Uncle Sam's. The threshold is $1 million for estate taxes in Massachusetts, New York, Oregon and Minnesota, and just $675,000 in New Jersey. Pennsylvania's and Iowa's inheritance taxes have no exemption in some cases.
However, all states allow surviving spouses to inherit tax-free from their partners, says James Walschlager, an estate-tax specialist at CCH, a unit of Wolters Kluwer.                                           
Only Delaware and Hawaii track the U.S.'s $5 million-plus exemption, according to Mr. Walschlager
Rates can be high as well. The top rate often is double digits, with Washington state's the highest: 20%.
                                  
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Most state exemptions aren't indexed for inflation, extending the tax's reach over time. "In Minnesota, many couples already have a $2 million net worth, and in 20 years even more will," says Gregory Gassert, a planner at Guardian Wealth Strategies in Minneapolis.
Are these taxes effective—that is, do they raise more revenue than they lose when residents like Mr. Negele decide go elsewhere? Economists are divided, and so are the states.
In recent years, several states have repealed or suspended their death duties, including Kansas, Oklahoma, Virginia, North Carolina and Indiana. Ohio's repeal, which took effect in January, was urged by Gov. John Kasich to help the Buckeye state "be more competitive with other states," says Gary Gudmundson, a spokesman for the state's tax department. Tennessee's estate tax is scheduled to disappear in 2016.
A few others have moved in the opposite direction. In 2011, Connecticut lowered its exemption to $2 million from $3.5 million. This year, Delaware rescinded the planned sunset of its estate tax, and Washington state raised its top rate on the largest estates for 2014. Minnesota imposed a gift tax beginning July 1 of this year, a move intended to prevent people from avoiding its estate tax by making large gifts while they're alive. (The only other state with a gift tax is Connecticut.)
For taxpayers facing state death duties, the challenge is clear: how to minimize or avoid them altogether. It's often possible to do so, experts say, but careful planning is required to avoid traps—especially for taxpayers who move to another state.
"It involves a lot more than being out of state for six months and a day per year," says Frank Sisson, an estate lawyer in Westport, Conn.
Expanded federal estate-tax benefits can also complicate planning for state levies. Here is what taxpayers navigating this maze need to know:
 
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Don't get burned by changing rules.
Married couples received a tax boon this past January when Congress retained the "portability" rules, which allow a surviving spouse to claim a partner's unused federal estate-tax exemption.
For example, if a woman dies before her husband in 2014 and leaves $1 million to other people, he could add her unused $4.34 million exemption to his own $5.34 million exemption for federal taxes, for total shelter of nearly $10 million of his assets. Before the portability rules were enacted, her unused exemption would have been lost if the couple hadn't set up special "credit-shelter" trusts.
However, such trusts still are necessary in many states with death duties. While assets would still pass to the survivor tax-free if there isn't a trust, at the second death the couple would lose the value of one of their two state exemptions, says Linda Hirschson, an estate lawyer at Greenberg Traurig in New York.
Existing trusts that haven't been updated to take account of portability could run another risk. Some have language specifying that an amount equal to the full federal exemption should go into a trust at the first spouse's death.
But if the state exemption is lower than the U.S. one, then the difference between the two could be taxable by the state because it isn't going directly to the survivor.
According to Ms. Hirschson, the New York tax resulting from this misstep would be more than $431,000 in 2014, on about $5.3 million of transfers.
Consider making gifts.
Because most states don't have a gift tax and the federal exemption is so large now, making gifts can be an efficient way to minimize state death duties.
Both cash and noncash assets can be given, but experts advise choosing carefully if the gift isn't cash. That is because the "cost basis" of a gifted asset carries over to the recipient.
For example, if a grandmother gives her grandson stock worth $40 a share that she bought for $10, then when he sells the shares he will owe capital-gains tax on any appreciation above $10.
In states with death duties but no gift tax, advisers sometimes recommend making large gifts after the death of the first spouse, giving assets that have benefited from the capital-gains-tax forgiveness at death. (Experts call this forgiveness the "step-up.")
Assume the grandmother in the example cited above dies holding her stock, which has grown from $10 to $40 per share. Due to the step-up, the cost basis rises to $40. If her husband inherits the shares and gives them to the grandson, the grandson would only owe capital-gains tax on the increase above $40 per share.
Under the best circumstances, Ms. Hirschson says, such assets pass to recipients free of both federal and state estate taxes, and with a higher cost basis likely to reduce future income taxes.
Connecticut and Minnesota—the only two states with gift taxes—follow the federal practice of allowing donors to make annual tax-free gifts up to $14,000 a year to any recipient.
For example, a married couple with three married children and six grandchildren could make 24 gifts of $14,000, for a total $336,000 a year, free of federal and state gift taxes—either outright or into a trust.
Gifts of tuition and medical expenses also can be tax-free if the check is written to the provider and not the recipient.
Be careful with out-of-state property.
                 
Death duties on assets owned by out-of-state residents can be tricky.
For example, some states could subject your summer home to their estate tax even if you live in a state without death duties—and it might not be possible to apply the state's entire exemption to shelter your property. Instead, the state could use a formula that calculates what percentage the property is of the total estate.
Others are more lenient. For example, New Jersey doesn't impose estate tax on in-state real property, such as a beach house, that is owned by out-of-state residents, says Samuel Weiner, a lawyer at Cole Schotz in Hackensack, N.J. But it could impose an inheritance tax on out-of-state heirs who aren't close relatives, he adds.
Connecticut's gift tax doesn't apply to transfers of out-of-state real property or tangible personal property, Mr. Sisson says: "A Connecticut resident could buy property in Florida, give it to a child and not owe gift tax here."
Moving to another state? Do it right.
For the tax-averse, the ultimate step is to pull up stakes and move. But this can be harder than it looks because of a legal concept known as "domicile," which refers to a taxpayer's true home.
Changing domicile for estate-tax purposes involves much more than spending time outside a state, although that counts. Among the other important factors are where a taxpayer votes; owns property; belongs to clubs; is a member of a church or synagogue; registers a car or boat; has minor children in school; has a professional license; and has a burial plot.
Experts say states are quick to challenge those who they think haven't really left. Mark Klein, a lawyer and New York state specialist at HodgsonRuss in Buffalo, says he scours the social media and press mentions of clients who are giving up New York domicile.
"State-tax auditors look at Facebook too, and I don't want them to see my client in an 'I Heart NY' T-shirt," he says.
Making the switch is often simplest for the ultrawealthy, says Dan Daniels, an estate lawyer at Wiggin & Dana in Greenwich, Conn., because "they already have several houses and can rearrange their affairs."
                               
        Advisers often warn against trying to change a domicile without selling the family home. "The cost of the controversy can be almost as much as the tax," says David Lifson, a certified public accountant at Crowe Horwath in New York.
Still, the concept of domicile includes quirks that taxpayers can use to their advantage. For example, it is possible for spouses to split their domicile. Both Mr. Sisson and Mr. Daniels advise couples in which one spouse is domiciled in Connecticut and the other in Florida.
A child who moves a legally incompetent parent into a state with an estate tax, perhaps to provide better care, also can successfully argue that there wasn't a change of domicile. "The parent didn't make the decision to move, so there's no domicile even though the person dies in the state," says Mr. Daniels, who prevailed in such an audit.
The other welcome news is that experts haven't heard of recent cases in which two states claim that one taxpayer is domiciled in both places. A spokesman for New York's tax department says it has resolved such conflicts when they do arise, about once a year.
This hasn't always been the case. After the 1930 death of John Dorrance, a Campbell Soup magnate, both New Jersey and Pennsylvania claimed he was domiciled there, and each billed his estate in full for millions in taxes.
Twice the U.S. Supreme Court refused to break the deadlock. After a multiyear battle, the estate paid tax to both states.
Write to Laura Saunders at taxreport@wsj.com