WASHINGTON (AP) _ The Supreme Court today agreed to hear the appeal of a Connecticut man who works in New York and wants the right to deduct alimony payments from his New York income taxes.

The court said it will study Christopher Lunding's argument that a state cannot bar out-of-state residents from taking deductions that in-state residents are allowed to take.

Lunding, a resident of Greenwich, Conn., works as a lawyer in New York City.

He and his wife, Barbara, reported a 1990 adjusted gross income of $788,210 on their federal tax form, with 48 percent of it coming from Lunding's work in New York.

That year, Lunding paid $108,000 in alimony to a former wife, also a Connecticut resident. On the Lundings' New York state income tax return, they deducted 48 percent of the alimony payment to match the share of their income that came from New York.

New York officials refused to allow the alimony deduction and told the Lundings they owed another $3,724 in taxes.

The couple sued the state, and a New York appeals court decided the state could not bar Lunding from deducting the alimony.

But New York's highest court ruled that the state can set different rules for in-state and out-of-state residents. New York residents are taxed on all income, no matter where they earn it, while non-residents are taxed only on income they earn in New York, the Court of Appeals said.

Lunding's alimony payments are ``wholly linked to personal activities outside the state'' and are not related to his New York income, the state court said.

In the appeal acted on today, the Lundings' lawyers said the state's policy violates the Constitution's requirement that states grant non-residents all ``privileges and immunities'' given to in-state residents.

The state's lawyers contended that New York can deny non-residents a deduction for expenses unrelated to their New York income.

The case is Lunding vs. New York Tax Appeals Tribunal, 96-1462.