Beacon Hill lawmakers seem to be on the verge of overhauling how they fund sheriffs offices across Massachusetts, in the wake of a state report that flagged an “opaque, chaotic and deeply flawed” financing process.

Inspector General Jeffrey released an initial report in February that said many of the state’s 14 county sheriffs overspend their budgets annually. That’s in part, the report said, because the Legislature regularly underfunds them in the main state budget, expecting to come back later in the year and add more money through supplemental spending bills.

Lawmakers asked Shapiro to review the sheriffs’ budgets after the sheriffs came to them with a request to cover a larger-than-usual $110 million deficit at the end of the last fiscal year.

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The Massachusetts House took a first stab last month at acting on the inspector general’s findings, and the Senate is now poised to take a similar step.

State representatives in April passed a $63 billion state budget that would reshape the funding for sheriffs’ offices. Instead of one lump sum for each office, the House’s budget for next year splits the $812 million in sheriff funding into four specific categories: operations, payroll, substance abuse treatment, and free phone calls for prisoners. Sheriffs, under the House budget, would no longer be allowed to keep spending once they’ve run out of money, and they’d need to tell state finance officials when they need more funds.

Top Senate Democrats unveiled their own budget plan Tuesday. Senate Ways and Means Chairman Michael Rodrigues said the spending bill he crafted “pretty much went along with what the House proposed” on sheriffs funding.

But he said the Senate wants to go “one step further” by setting a rule that if any sheriffs aren’t providing state finance officials with the necessary information, a fiscal control board would be able to step in and take over managing their budgets.

While the House and Senate have some common ground on sheriff funding reform, the two chambers diverge on some other funding and policy matters.

Senate leaders added an outside section into their budget aimed at reducing the hassle of canceling subscriptions. That policy was not included in the House’s bill.

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The proposal would require online streaming services and other companies to make it as easy to cancel a subscription as it is to sign up for one. Senators say the change, similar to language Gov. Maura Healey included in her initial budget proposal, would align state law with consumer-protection regulations put in place by Attorney General Andrea Campbell’s office.

Rodrigues said the subscription measure would save people “not money, but aggravation.”

Increases to local aid

As cities and towns across the state weigh property tax hikes or service cuts, the Senate is proposing a bigger boost to local aid than the House.

The Senate budget proposes a $53 million increase in direct, flexible state aid to cities and towns, well above the House’s $10 million bump up for that account.

Senate President Karen Spilka says the extra money will help municipal governments address rising costs.

“They handle a whole variety of social service programs, police, fire, schools, DPW, public safety, so many different areas, and it really touches every aspect of the quality of life of every single resident of our commonwealth,” she said.

House lawmakers set aside another $10 million in their budget to help school districts that have faced unexpected drops in student enrollmentamid heightened enforcement of federal immigration policy. Rodrigues said the Senate did not take that same step in its budget.

The state Senate plans to kick off debate on its budget on May 18. After senators pass their version of the spending plan, they’ll start closed-door talks with the House in hopes of agreeing on a final budget by July 1, when the new fiscal year starts.