We agree with legislators calling for a multi-pronged, independent investigation of reported overtime abuse and other improprieties by the Massachusetts State Police. That is the only way to restore credibility and ensure adequate oversight of an agency that traditionally has been secretive in concealing its records from the public.

Language in the state budget approved Thursday by the House seeks three components to an investigation of state police practices: creation of an independent audit unit directed by the state’s inspector general; establishment by the Legislature of a commission to review hiring and promotion practices; and a review by experts at the University of Massachusetts Boston of the state police management structure.

“These provisions will monitor the agency, help develop best practices and help prevent issues from occurring in the future,” said state Rep. Jeffrey Sanchez, D-Boston, chairman of the House Ways and Means Committee.

That investigation would examine reports that at least 30 state troopers in the division that patrols the Massachusets Turnpike were paid overtime for shifts they did not work in 2016, and that the state comptroller since 2010 had not received the required payroll records for another troop assigned to Logan International Airport in Boston.

In addition to the questionable pay practices at the state’s largest law enforcement agency, involving millions of taxpayers’ dollars, leadership of the state police has been under fire. Its top two commanding officers, Richard McKeon and Francis Hughes, retired in November amid an investigation of why an arrest record for a judge’s adult daughter was altered. McKeon was accused of ordering a trooper to remove information from the report to protect the judge and his daughter, who police say failed sobriety tests after an accident in October.

The measures proposed by the House would broaden the investigation underway by the attorney general’s office to determine if criminal charges should result from the alleged no-show overtime shifts.

And the House initiatives would be more far-reaching than the reforms announced earlier this month by Gov. Charlie Baker and the state police commander, Col. Kerry Gilpin. Those policy changes include activating existing GPS locators in cruisers to track state troopers — which is a common-sense safety measure — and disbanding Troop E, which was responsible for the alleged overtime abuse. Those troopers will be reassigned and the responsibility for patrolling the 138-mile turnpike will be split among other divisions.

An internal audit last month showed that 30 active and retired troopers assigned to Troop E may have been paid overtime for unworked shifts. Some of those troopers already have been suspended without pay while an internal affairs investigation continues.

The names of the state police under investigation have not been made public, and their ranks range from trooper to lieutenant. Gilpin also has not specified how much the questionable overtime totals, though she said the number of shifts per trooper being investigated is between one and 100.

The Boston Globe last month reported that $46.4 million — or 15 percent of the state police payroll — was spent on overtime last year. According to the Globe, 299 troopers — or nearly 14 percent of the state police force — earned more than $200,000 in 2017, as the result of overtime shifts and private details directing traffic or providing security at events, on top of their base pay. The Globe reported that the median pay for a state trooper last year was $145,413, slightly less than the governor’s salary of $151,800.

Some of the highest-paid troopers work for Troop F at the airport and Seaport district in Boston. Payroll records for that division were released after the Globe raised questions about why they had not been filed with the comptroller’s office since 2010.

According to the Globe, total pay for the 140 troopers assigned to Troop F accounted for $32.5 million last year because of extensive overtime, and at least 79 percent of them made more money than the governor.

“The Massachusetts State Police have a long and honorable history,” Baker said earlier this month. “The men and women who have worked there for generations earned that honor. That history, that reputation, has been tarnished.”

We agree. It will only be restored with a full, public accounting of any improprieties by state police, and leadership by state officials to ensure that the problems are fixed.