Republicans wasted little time Saturday seeking to capitalize on Senate Finance Chairman Max Baucus’ (D-Mont.) admission that he had a personal relationship with his former state director, as the Republican National Committee called on the Senate Ethics Committee to launch an investigation.

In a statement released Saturday afternoon, the RNC accused Baucus of using “his Senate office to advance a taxpayer funded appointment for his staff-member girlfriend— and complained the issue “raises a whole host of ethical questions.—

Baucus on Friday night released a statement confirming that he had recommended his girlfriend and former state director, Melodee Hanes, to be appointed U.S. attorney for Montana. Hanes later withdrew her name from consideration for the post, and took a job with the Justice Department in Washington, D.C., so she could move in with the Senator.

The RNC — which has remained silent through the months-long scandal involving Sen. John Ensign’s (R-Nev.) relationship with a former campaign aide — called for the Senate to schedule hearings on Baucus’ recommendation that Hanes get the appointment.

“This issue demands the attention of the Senate Ethics Committee. They should hold a hearing to identify who was involved in this process, what they knew and when they knew it, and why Senator Baucus put his personal needs above those of the people of Montana,— the RNC statement said.

The committee did not indicate what rules it believes Baucus may have broken, and Senate Minority Leader Mitch McConnell (R-Ky.) refused to comment on the affair Saturday. A preliminary review of federal law and Senate Ethics rules by Roll Call did not reveal any basis for a potential violation at this point.

Baucus’ office late Friday acknowledged he has had a relationship with Hanes, his former state director since the summer of 2008, when Hanes was still working for him. Baucus had been separated from his ex-wife for several months when the relationship began, and Hanes was already divorced.