A Massachusetts legislator is calling for an investigation of compensation and benefits provided to leaders of state universities and colleges, saying Thursday that the perks are “unsustainable and irresponsible.”

State Sen. Ryan Fattman, a Republican from Webster, wants the Senate Post Audit and Oversight Committee to examine policies that let top administrators cash out significant numbers of rolled-over vacation and sick days when they retire, and what he called “extravagant” benefits including housing and car allowances, country club dues, and free tuition for spouses and children.

“It’s not right to be financing all of this on the backs of our students,” said Fattman, who sits on the committee. “Kids are coming out with huge amounts of debt, and now we’re finding out they’re paying for these perks.”

Also Thursday, a spokeswoman for Gov. Charlie Baker said the governor was “disappointed” to learn about “excessive benefits and bonuses” at state universities and colleges. Press secretary Lizzy Guyton said Baker “believes they should do more to practice fiscal responsibility” and “urges all higher-education institutions to take steps to tighten their belts.”

Baker and Fattman were responding to an investigation by the New England Center for Investigative Reporting and published on its website and local and regional newspapers. Fattman also cited recent reports of large sums being paid to departing university and college presidents.

Most presidents of community colleges and state universities and chancellors of the University of Massachusetts campuses get houses or housing allowances and cars or car allowances, and are eligible for six months’ to one year’s pay if they are fired without cause, the New England Center reported. Several of the UMass leaders, if they quit, can elect to return to faculty jobs at guaranteed earnings of between $240,000 and $480,000, first taking one-year sabbaticals at the same salaries they received as chancellors. They also get free tuition for themselves, their spouses, and their children.

Many of these benefits are typical in higher education. Some also are extended to other Massachusetts university and college faculty and a few to other state employees. But as college costs rise, and examples have emerged of large payouts, the perks have come under increasing scrutiny.

The state Department of Higher Education already is investigating a policy that lets community college and state university administrators and other employees convert vacation days into sick days and cash them out for as much as 20 percent of their value. That happens once they’ve saved up more than 64 unused vacation days, the maximum they can collect, for which they earn 100 percent.

Bridgewater State President Dana Mohler-Faria received $269,984 for carried-over vacation and sick days when he retired, the Boston Business Journal first reported.

Former Middlesex Community College President Carole Cowan and Vice President Jay Linnehan received a combined $440,581 in accrued sick and vacation days plus severance and early retirement incentive pay, the Lowell Sun found.

The disclosures come at a difficult time for universities and colleges, which have been pushing for an increase in their state budget allocations.

“There’s been a lot of attention about the request for more money for higher education,” said Eileen McAnneny, president of the nonpartisan, Boston-based Massachusetts Taxpayers Foundation. “The legislature has a right to ask how that money will be spent, and that it’s used for the best and most appropriate purposes.”

She and Fattman also said they want to know why the public is not entitled to see the goals based on which the chancellors of the University of Massachusetts campuses can earn annual performance bonuses of up to $71,012 at UMass Boston and up to $201,000 at the UMass medical school. The office of UMass President Marty Meehan says these goals are part of the chancellors’ personnel files, and therefore not public.

“If you’re working for a public institution there should be an expectation that that information will be public,” McAnneny said. “Taxpayers deserve at least that.”

University officials and defenders of the compensation packages have said they’re necessary to compete for the best leaders. But Fattman was dubious. “You cannot convince me that having generous sick leave and vacation buyouts on the taxpayers’ dime is going to make us a more competitive in higher education,” he said.

Some faculty also were critical. Joseph LeBlanc, president of the Massachusetts Community College Council, said that even though faculty and other employees get some similar benefits, it’s not “near the sweetheart deals it appears some of the public higher education presidents are getting.” He said, “It’s not like they’re some kind of corporate CEOs here. It’s just ridiculous.”