As Gov. Andrew M. Cuomo pushes lawmakers to disclose more about the income they earn in part-time jobs, Republicans in the New York Senate have drafted legislation that would expand the spirit of that disclosure to the governor’s girlfriend, the celebrity cook Sandra Lee.

New York’s state officials are already required to disclose financial information about their spouses, including their spouses’ income and investments. The new proposal, introduced on Thursday by the Republican majority in the Senate, would expand the disclosure requirements to include anyone who resides with a public official, whether or not they are married. Mr. Cuomo, a Democrat, and Ms. Lee share a home in Westchester County.

The governor’s office responded in part by suggesting that if Ms. Lee had to reveal her income, so should the paramours of married state legislators.

Mr. Cuomo has called on lawmakers to enact stricter financial disclosure rules after the January arrest of Sheldon Silver, who was subsequently forced to resign as the State Assembly speaker. Mr. Silver, a Manhattan Democrat, is accused of taking payoffs disguised as legitimate income from practicing law.