ALBANY — In late February 2016, the Republican leader of the New York State Senate, John J. Flanagan, sent a letter to the chamber’s secretary outlining a series of stipends to various members — de facto bonuses totaling hundreds of thousands of taxpayer dollars.

In that letter, Mr. Flanagan said the stipend for the chairman of the Health Committee should be paid to Senator David J. Valesky, an upstate member of the Independent Democratic Conference, an eight-member breakaway group whose alliance with the Republicans has kept that party in power in the Senate.

There was just one catch: Mr. Valesky was not the chairman of the Health Committee.

Instead, he was the vice chairman; the actual chairman of that committee, Senator Kemp Hannon, a Republican from Long Island, was awarded a richer bonus for a different Senate leadership position, and by law, lawmakers can receive only one such stipend, commonly known as a lulu.

Two weeks after Mr. Flanagan’s letter, Mr. Valesky was identified as “chairman of senate health committee” in documents sent to the state comptroller by the Senate payroll staff, a designation that was false, and Mr. Valesky was later paid the $15,000 stipend. On Saturday, a Senate lawyer said those documents were simply “accounting papers.”

State law does not explicitly allow for a Senate committee vice chairman to be paid a stipend or for a chairman to pass along the stipend to another member. Moreover, presenting false documents to a public official with the intent to defraud the government can be a felony, a crime known as filing a false instrument.

Over the weekend, however, Senate lawyers argued that the Senate’s actions were legal, constitutionally defensible and proper as “a classic example of internal administrative prerogatives.”

As part of its case, the Senate presented documentation that Mr. Flanagan was not the first Senate leader to direct chairman payments to vice chairmen; in March 2015, his predecessor, Dean G. Skelos, another Long Island Republican, directed that Mr. Valesky receive a stipend.

In a four-page memo released late Saturday night, the Senate’s top lawyer, David L. Lewis, argued that the documents sent to the comptroller with the false information were “accounting papers” and that the titles were used as a way to ensure payment, not to lie about the position they held.

“The practice has been to assign to the member the statutory title to identify the amount to be paid,” Mr. Lewis wrote, “and not to assert that the member holds the specific office.”

That process — in which a vice chairman was presented as the chairman so as to be eligible for the stipend — was repeated many times to pay tens of thousands of dollars to other political allies of Mr. Flanagan, including two other members of the breakaway Democratic group and at least three upstate Republican senators.

All told, Senate payroll certifications to the comptroller, as reported last week by The New York Times, resulted in authorization for payments to at least six senators: Mr. Valesky, of Syracuse; Diane Savino, Democrat of Staten Island; Jose Peralta, Democrat of Queens; Thomas F. O’Mara, Republican of the Finger Lakes; Patrick M. Gallivan, a Republican who represents an area east of Buffalo; and Patty Ritchie, a Republican who represents an area north of Syracuse.

In emails to the comptroller, all were identified as chairmen or chairwomen of committees they did not lead. A seventh senator, Senator Pamela Helming, a first-term lawmaker from Central New York, was also misidentified in the Senate payroll documents as a chairwoman, but her office said she did not accept the payment connected to that designation.

The practice has outraged some good-government groups, which have called for investigations by law enforcement, and emboldened political opponents of Senate Republicans and the Independent Democratic Conference, sensing a weakness in the ruling coalition.

“The Republican ‘memo’ is an obvious after-the-fact effort to cover up for an outrageous misuse of taxpayer funds,” said Mike Murphy, a spokesman for the Senate Democratic Conference. “The diversion of legislative stipends to those not entitled to them is illegal, as are the false filings provided to the comptroller.”

As the Independent Democratic Conference has argued, Mr. Lewis, the lawyer, said he believed that stipends paid to vice chairmen or vice chairwomen were allowed by a clause in legislative law that refers to senators serving in special roles or “directly in connection therewith.” But that clause continues to say that those special roles “shall be paid an allowance in accordance with the following schedule,” and it then specifically details payments for chairmen and ranking members of committees. It makes no mention of vice chairmen of Senate committees.

Still, Mr. Lewis wrote, the law does not limit “what offices may be created by the Senate” and “does not specifically require that the Senator hold that office but only that he or she acts directly in connection therewith.”

Mr. Lewis also noted “years of documentation that have followed the same practice” of passing along stipends, including Mr. Skelos’s letter ordering Mr. Valesky’s stipend.

It was dated March 2015, nine months before Mr. Skelos was convicted on separate federal corruption charges.