The state Senate is opening an investigation into the de Blasio administration’s exporting of New York City homeless families to other parts of the state, The Post has learned.

It was discovered last week that the city is paying a year’s rent to encourage the homeless to ditch the Big Apple’s homeless shelters for apartments upstate.

Senate Investigations Committee Chairman Terrence Murphy (R-Hudson Valley) told The Post on Sunday that he’s opening a probe and will hold a public hearing on the matter after being briefed by an infuriated state Sen. Fred Akshar, who represents the city of Binghamton and Broome County, where the homeless are being shipped by the city.

“It’s very concerning when people are relocated from one part of the state to another without community notification,” Murphy said. “It’s slap in the face. It’s sleight of hand. I wouldn’t expect anything less from Mayor de Blasio.”

This is not the first time the two politicians have butted heads. The mayor raised money in 2014 to try to help a Democratic candidate topple Republican Murphy. But Murphy won.

“A lot of questions need to be answered,” Murphy said. “Let’s be open and honest about it. Why is New York City paying people to move to Binghamton without anyone knowing about it? Do these people have criminal records? Did they just get out of jail? Or are they just out of luck?”

Broome County welfare officials found out about the families when they came into the Social Services office to apply for other benefits but not rental subsidies. They were told New York City had already taken care of their rent.

Alarm bells went off.

Akshar, a Republican, said it’s not just about his district.

“This could be happening in Rocehster, Buffalo, Albany, you name it,” he said.

“Bill de Blasio is putting homeless New Yorkers on buses, tossing them some rent money and sending them elsewhere . . . for someone else to take care of,” Akshar added. “The people of the Southern Tier and Broome County support and take care of their own in good times and bad. We don’t ship our struggling neighbors elsewhere for others to ‘deal with’ and call ourselves progressives.”

There are 800 families consisting of nearly 2,600 people who have utilized the Special One Time Assistance, according to the city Department of Homeless Services. About one-third have found housing within the five boroughs, ten percent relocated to other parts of New York state and more than half have found housing outside the state, the department reported.

More problematic for City Hall is that the controversy has ticked off fellow Democratic lawmakers from upstate.

“The Special One Time Assistance Program (SOTA) is a disservice to individuals and families who are homeless in NYC,” said Assemblywoman Donna Lupardo (D-Broome).

“This type of ‘assistance’ feels like something else entirely,” Lupardo added. “ ‘Out of sight, out of mind’ is no substitute for a comprehensive strategy to address the shortage of affordable housing.”

Broome County officials claim the program is illegal because it violates a state law that prohibits a person being sent “into a public-welfare district with the purpose of making him a charge on such public-welfare district.”

But the city Department of Homeless Services maintains that the program is not illegal because it’s voluntary.

“This is not a new program. For decades, the City has helped homeless families who find affordable housing and employment outside of the City relocate. We hope these communities will welcome these families as they work to get back on their feet,” said mayoral spokeswoman Jaclyn Rothenberg.