A growing list of public officials in high-tax states are expressing alarm that big earners are bolting to low-tax states as new data suggests some home buyers are moving in response to the year-old change in the federal tax law.

New York Gov. Andrew Cuomo became the latest on Monday when he blamed a $2.3 billion state shortfall on the new federal tax law that he said is driving people to leave the state. During a news conference in Albany, Mr. Cuomo said the 2017 law capping a deduction for state and local taxes at $10,000...