A day after three state troopers were charged with embezzling public funds, Massachusetts senators who sit on an oversight panel said they don't plan on taking a look into the troubled law enforcement agency.

State Sen. Kathleen O'Connor Ives, chair of the Senate Post Audit and Oversight Committee, said her panel has its "plate full."

She pointed to its recent reviews of a MBTA proposal to privatize busing and maintenance facilities and the UMass Amherst purchase of Mount Ida, a campus that until earlier this year a private college in Newton.

"The State Police situation is so huge in terms of its seriousness and potential criminality, that it's actually beyond the scope of this committee, because we have the resources that we have and other topics on our plate, and it needs to be incredibly thorough," O'Connor Ives, a Newburyport Democrat, told reporters after the committee released its report on the controversial Mount Ida acquisition.

The committee is "always going to be happy to play a role if it's responsible and relevant," O'Connor Ives said. "But to be able to say that we're involved in this, just so that we can say that we are, wouldn't be responsible."

The committee has seven members and subpoena powers.

"We do have other issues we plan on taking up," O'Connor Ives said. "The State Police will not be one of them because it's so massive in its responsibility and response to what has been done in terms of breaking the law that it's actually beyond our responsibility and jurisdiction."

Sen. Michael Moore, a member of the oversight panel and Senate chair of the Legislature's Public Safety Committee, noted that Gov. Charlie Baker replaced the superintendent in charge of the State Police, installing Col. Kerry Gilpin to deal with cleaning up the agency.

"They've taken swift action," said Moore, a Millbury Democrat.

Lawmakers on the House side proposed a new audit unit within the State Police. The proposal, tucked into the House version of the state budget, also includes a new commission to review the agency's hiring and promotion practices.

House and Senate lawmakers are hashing out differences in the proposed state budget for the coming fiscal year before sending the final version to Baker's desk for review.

Federal prosecutors and Attorney General Maura Healey have both launched separate investigations into State Police troopers' alleged overtime abuse and embezzlement. The arrests of three troopers on Wednesday are just the beginning of the investigation, US Attorney Andrew Lelling told reporters.