By Jimmy Vielkind

ALBANY, N.Y.--The New York State Police budget and head count grew during Gov. Andrew Cuomo's nine-year tenure while other state agencies shrank--an expansion that is being questioned as protesters around the state seek to change policing practices.

Mr. Cuomo, a Democrat, has steadily increased funding for the agency, whose troopers and investigators patrol all areas of the state. They are particularly important in upstate areas where there is no municipal police force, but Mr. Cuomo pushed the agency during his second term to expand its presence in New York City.

The agency's operating budget grew by $117 million from when Mr. Cuomo took office in 2011 to the fiscal year that ended in April. It has added 350 employees in that time, according to state budget documents.

Other state departments' budgets remained static or decreased over the period. State agencies that oversee public health, tax collection, correctional facilities and mental-health care have all shed employees since 2011, records show.

State officials said these declines were in part explained by the consolidation of information technology services to a single agency. But E.J. McMahon, research director for the Empire Center, a fiscally conservative think tank, said the State Police "definitely have most-favored-nation status."

The state budget signed by Mr. Cuomo in April froze the allocation for school aid and cut Medicaid reimbursement rates for hospitals. The State Police operating budget increased to $811 million from $774 million in the fiscal year that ended in April.

State Sen. Zellnor Myrie, a Democrat from Brooklyn, was pepper-sprayed by police during a May 29 protest in Brooklyn over the death of George Floyd, a black man who was killed in Minneapolis police custody after a white officer knelt on his neck.

Mr. Myrie said it was time to rethink the funding allocation.

"There are no sacred cows," Mr. Myrie said. "I would love to see the money that got cut from the hospitals in the middle of a pandemic--if we can find savings in the State Police department, we should do that."

Mr. Cuomo hasn't embraced calls by protesters to defund the police. On Friday, he signed an executive order requiring police departments around the state to review how their practices affect communities of color. Municipalities must come up with a plan to address disparities by April 1, 2021, or face the loss of an unspecified pool of state funding.

"Start with a blank sheet of paper and come up with your vision for your public-safety department in your community," Mr. Cuomo said Wednesday. "People talk about defunding the police. What is the budget that you want for the police?"

He previously said his administration would undertake a similar process for the State Police. The governor also signed a bill Tuesday that will require troopers, by April, to wear body cameras while on duty. The State Police don't currently use body cameras, which were first introduced to the New York Police Department in 2017.

Richard Azzopardi, a senior adviser to the governor, said the increased State Police funding was partly due to labor contracts, as well as initiatives to combat hate crimes, gang violence and sexual assault. He said head counts were depleted because former Gov. David Paterson didn't authorize funding for new academy classes in the aftermath of the 2008 financial crisis.

It also reflects the 2016 deployment of more than 150 troopers in New York City. They are posted at bridges and tunnels as well as transit hubs, according Thomas Mungeer, president of the New York State Troopers Police Benevolent Association.

Mr. Mungeer said Mr. Cuomo had steadily increased funding for the State Police over his three terms, and said he fulfilled requests to purchase new patrol cars and rifles for troopers.

Patrick Phelan, chief of the Greece Police Department in suburban Rochester and president of New York State Association of Chiefs of Police, said his organization wasn't consulted about Mr. Cuomo's executive order. He said engaging community stakeholders is always a good thing, but worried it could boil down to an unfunded mandate.

Both Mr. Phelan and Peter Kehoe, executive director of the New York State Sheriffs' Association, said there is very little direct state funding to police departments. Most allocations are for traffic-safety enforcement, they said.

"Rather than defund the police, what we need to do is make a massive investment in training. Because there are opportunities to make sure our officers are better trained, particularly when it comes to the use of force and de-escalation techniques," Mr. Phelan said.

Protest organizers say funding should move in the opposite direction. Joo-Hyun Kang, director of Communities United for Police Reform, is pushing officials to decrease funding for the NYPD in the coming city budget but said the groups in that coalition will soon turn their attention to the state.

"This is not the time to be expanding," she said.

Write to Jimmy Vielkind at Jimmy.Vielkind@wsj.com