ALBANY – Don’t sue me, I’ll sue you.

More than a dozen New York sheriffs filed suit over an anti-ICE sanctuary state law that took effect Tuesday — as Gov. Kathy Hochul demanded local governments stop cooperating with the feds or face their own legal troubles.

Hochul herself vowed to sue localities such as Nassau County — where her Republican gubernatorial rival Bruce Blakeman serves as executive — that refuse to end cooperation agreements with US Immigration and Customs Enforcement.

But the federal lawsuit led by Rensselaer County Sheriff Kyle Bourgault contends the law, signed by Hochul in May, is unconstitutional and wrongly impedes local officials, notably sheriffs, from making public safety decisions.

“Today, Kathy Hochul escalated her administration’s war on the police and she expanded polices to put criminals before the citizens of New York,” said Rensselaer County Executive Steve McLaughlin.

The governor held a press conference in Albany earlier Tuesday to tout the start of the “Local Cops, Local Crimes Act” — arguing it’ll keep New York police agencies focused on criminal cases, rather than helping the feds’ work of civil immigration enforcement.

“Any police department or sheriff’s office that disobeys this law, that maintains any agreement with ICE, will face legal action,” Hochul declared from a podium in her ceremonial office in the state capitol.

“And to those suing us, those trying to block the implementation of this law who’ve tried before and failed, our law has already been upheld by the courts, but if you try me again, I say, ‘Bring it on.’”

Blakeman, during his own news conference, which took place at the same time as Hochul’s but in Delaware County, declined to say whether he would comply with the new mandate.

He later told The Post he’d “probably” join the sheriffs’ lawsuit.

His running mate for lieutenant governor, Madison County Sheriff Todd Hood, is among the 15 plaintiffs on the case, which names Hochul, New York Attorney General Letitia James and the state as defendants.

But the AG made clear she viewed Blakeman’s inaction so far as defiance — and her office on Tuesday issued multiple subpoenas to Nassau County and its police department demanding details on their deal with ICE.

Known as a 278-g agreement, the Blakeman-brokered deal set aside 50 jail cells to house federal immigration detainees — a cooperative arrangement touted by the GOP pol as necessary for public safety.

Roughly a dozen or so counties and municipalities also had entered into 278-g agreements with the feds, mostly centered around using their jails to hold detainees for ICE.

But Hochul, a Democrat, moved to scotch the deals amid a backlash against heavy-handed tactics by ICE nationwide — and the back-to-back killings of Renee Nicole Good and Alex Pretti by feds in Minneapolis.

The governor, who is seeking re-election to a second, full four-year term in November, pitched banning the local agreements on top a mix bag of other anti-ICE measures earlier this year.

The Democratic-led state legislature complied.

James’ staff also sent out subpoenas to the sheriffs’ offices in Broome, Steuben and Rensselaer counties — where officials hadn’t yet confirmed whether they’d comply with the law.

Broome and Steuben County officials later indicated they would end their agreements, but the former’s sheriff, Frederick A. Akshar, was also a plaintiff on the suit. Hood has also previously said he’d end Madison County’s deal with ICE.

Bourgault, the sheriff for Rensselaer County, emphasized his agreement only pertains to the local jail and allows guards to run detainees through a federal database to see if they’re wanted on immigration offenses.

“Our deputies are not out driving around looking for undocumented immigrants. They are not conducting immigration checkpoints,” he said. “They are not making immigration-related traffic stops. They are not riding around our communities with ICE agents looking for people to arrest.

“Our participation occurs inside the Rensselaer County jail, and let me say it again, involving individuals who have already been arrested.”

Most of the counties with 287-g agreements are similarly focused on jails, Bourgault said.

But Nassau County’s deal also deputizes local law enforcement officers, authorizing 10 trained detectives to perform certain immigration enforcement functions.

Blakeman, when asked by The Post last week if he’d follow the new law, said he was checking his options with his attorneys and that he hadn’t decided yet if he’d comply, ignore the mandate entirely, or take it to court.

Hochul, for her part, danced around specifics Tuesday on how she would fight if Blakeman refuses to wind down his agreement.

“No county executive should think that they are above the law in the state of New York,” she said.

“However, if they do thwart the laws that are duly enacted by this legislature and the governor, the Attorney General will be fully responsible for enforcement.”

A US Department of Homeland Security spokesperson argued that nearly 7,000 immigrants with criminal records were released in New York because of the state’s failure to honor ICE detainers.

“Governor Hochul must stop putting politics above public safety,” the spokesperson said. “This type of insanity leads to more crimes and more innocent victims.”

— Additional reporting by Josh Christenson