Ms. Giove added that the I.D.C. believed that case law backed its argument, and that the law itself “supports allowances for vice-chairs who are ‘directly connected therewith’ to committees in our house.” Senate Republicans similarly maintain that everything was done in accordance with the law.

But good-government watchdogs said that such a justification circumvented the intention of the law, which was meant to reward chairmen for extra work.

“They’re doing an end run around the system,” said Blair Horner, the executive director of the New York Public Interest Research Group. “They’re supposed to be getting extra compensation for additional work. And if that’s not what’s happening, they’re completely undermining that argument.”

The arrangement appears to have been signed off on by Senate Republicans: The Senate leadership is responsible for providing and entering the information on chairmanships into the state payroll system, according to the state comptroller’s office.

Under state law, the leaders and ranking members of most of the Senate’s nearly three dozen committees are given extra payments — commonly known as “lulus” — ranging from $9,000 to $34,000 a year. By law, legislators can receive only one such stipend, and lawmakers typically take the greater stipend if they hold multiple leadership positions.

The money is an important perk. Lawmakers receive a base salary of $79,500 a year. The Legislature has not had a pay raise since 1999; their attempts to be paid more have been bogged down in disputes over banning outside income and other ethics-related changes.