For decades, New York lawmakers have groused about the state’s process for crafting an annual budget, arguing it hands too much power to the sitting governor.

This year, with a new governor at the helm, they’re hoping to do something about it.

The state Assembly’s Democratic majority released its budget proposal over the weekend, laying out a wish list of proposals and items that should be financed for the fiscal year beginning April 1.

But the legislative conference stripped out several major priorities of Gov. Kathy Hochul, which the Democratic governor included in her $216 billion budget plan in January. Among them were a four-year extension of mayor control of the New York City school system, as well as a measure that would permanently give bars and restaurants the ability to serve to-go cocktails and wine, stoking the ire of the liquor lobby.

The message from the Assembly lawmakers was clear: The budget should be about the state’s finances, not whatever policy proposals a governor seeks to advance, a tactic that’s been employed for years.

Speaking with reporters Monday afternoon at the Capitol, Assembly Speaker Carl Heastie, a Democrat representing the northeast Bronx, said it wasn’t personal.

“I’m not trying to send Governor Hochul a message,” Heastie said. “I’m just relaying the feelings and sentiments of the conference that they just want to put forward a fiscal document. The policy discussions, we’re open to having them. But the presenting of the (budget) resolution is just about the state’s finances.”

New York’s process for setting a state budget is laid out in the state constitution and has been in place since the early 20th century. The governor is essentially the biggest driving force behind what makes the cut and what’s left out.

Every January, the governor is required to put forward a budget plan. The state Legislature, meanwhile, faces constitutional restrictions about what it can change. Generally, the Legislature can reduce or eliminate particular lines appropriating money, but can’t add to them.

Along with the appropriations, the governor also lays out a series of bills that would change portions of state law, ostensibly to make changes to things such as tax policy or other items that would have an impact on the budget.

But governors have used those bills to propose any number of policy priorities at a time when their leverage over lawmakers is greatest. Under Gov. Andrew Cuomo, the state enacted everything from cash bail reform to voting reforms to limousine safety laws through the budget process. Notably, he inserted Raise the Age into the budget in 2017, diverting 16- and 17-year-olds accused of a crime away from criminal court and to family court.

In Hochul’s budget proposal – her first after succeeding Cuomo in January – she included at least a handful of policy issues that had little to do with the state’s finances.

Most notable was mayoral control of New York City public schools. Since Mayor Michael Bloomberg wrested control of the city’s school system from a series of now-defunct boards in the early 2000s, state lawmakers have reauthorized that authority every few years – a process that has required Mayors Bloomberg, Bill de Blasio and now Eric Adams to seek Albany’s approval.

The latest authorization expires in June. And Hochul included a four-year extension in her January budget proposal. But both the Assembly and Senate’s budget proposals didn’t include the extension.

Asked on Saturday about lawmakers not including mayoral control in the budget, Adams said leaving the decision dangling until June “is just not the right thing to do.”

“So we were going to continue conversations with our colleagues,” Adams said. “We're happy the Governor understands how important this is. And we're looking forward to asking them continuously. Let's put this in the budget.”

For Heastie, it was about sticking to his conference’s no-policy-in-the-budget stance. Lawmakers are scheduled to be in Albany into June, he noted.

“It’s always been the Assembly’s position to advance mayoral control,” Heastie said. “I wouldn't get nervous that it's not in the (Assembly budget) resolution. It doesn't expire till the end of June.”

E.J. McMahon, founding senior fellow of the Empire Center, a fiscally conservative think tank, said he doesn’t agree with much of the Assembly Democrats’ agenda. But he said from an institutional standpoint, Heastie is taking an important stand.

Unrelated policy items “are not needed to be done as part of the budget,” said McMahon, who has written extensively about the history of the state’s budgeting process. “There's no reason that they can be or should be and it clogs up the process. The issue is the budget, not (Hochul’s) desire to extend mayoral control of the schools.”

Hochul said she anticipates seeing some of her policy plans in the final budget, which is due March 31 after extensive negotiations.

“Yes, we’ll have policy in the budget, I believe,” Hochul said Monday.

The governor said there is precedent for policy proposals in the budget, pointing to recent budget cycles led by Cuomo. And she expects that to continue now that she’s in office – especially because the annual legislative session will end in early June this year as the state primaries are scheduled for June 28.

“I believe that it makes sense, especially because we have a shortened timeframe,” Hochul said. “The Legislature plans on leaving early in June and we want to get it all done. We have a lot of ideas that we believe that we can work through with the leadership.”

Like the Assembly, the Senate’s Democratic majority also stripped Hochul’s proposals regarding mayoral control and to-go cocktails from their budget plan. But Senate Majority Leader Andrea Stewart-Cousins, D-Yonkers, said she’s not necessarily opposed to tackling policy issues in the budget.

“We’ve obviously done different policies in the budget before, so we're not opposed to all policy being removed,” Stewart-Cousins told reporters Tuesday. “But some are easier than others. And, listen, I'm willing to have a discussion about what can be done and what cannot be done in the budget.”

Speaking to reporters, Hochul seemed open, at least, to tackling the issue of mayoral control after the budget process is finished.

“I just want to get it done,” she said. “We’ll let everybody know what the timing is.”