A violent illegal immigrant who repeatedly sneaked into the US has now been linked to a slew of rapes in the Bronx and Westchester County — but there’s nothing authorities can do about it.

That’s because the statutes of limitations on the rapes expired by the time the suspect’s DNA was tested, likely thanks to a backlog in cases, law enforcement sources told The Post.

“We can’t go back and charge him — it’s screwed up,” a frustrated source said.

Adding to the mess, the victims “might never, ever know his identity’’ because the cases are now considered closed, the source added.

The saga of criminal Ronald Clare Greenland, 54, began when he first sneaked into the US from Jamaica in the 1980s, sources said. He eventually committed crimes from auto theft to arson and even assaulted a cop, spending several stints in prison.

Immigration and Customs Enforcement said it tossed him out of the country in 2009 by putting him on a plane back to Jamaica.

But he somehow stole back into the US and had more run-ins with the law.

In 2015, ICE booted him again.

And again, Greenland sneaked back in.

Then in November, Westchester cops spotted him allegedly breaking into a car dealership and prying the rims off a car. When officers gave chase, Greenland pulled out a knife and slashed and stabbed Police Officer David Sanchez multiple times in the chest, authorities said.

Sanchez survived the attack only because he was wearing a Kevlar vest, officials said.

Sources said Greenland was likely swabbed for his DNA during past prison stints. Rape kits preserve hair, saliva and semen off sexual assault victims.

But not all of the samples that were collected in the 1990s were immediately tested. In 2015, there was still such a backlog of untested kits that the Manhattan District Attorney’s Office spent $38 million to clear them.

Either way, Westchester authorities took fresh samples from Greenland when they booked him for the attempted murder of the cop. They ran his DNA through the system — and came up with a slew of hits to local rapes, sources said.

But it was too late.

Because the rapes occurred in the 1990s, when the statute of limitations on such crimes was only five years, authorities say they can’t prosecute him for the crimes.

A source with the Westchester County District Attorney’s Office said cops are now left to search for other possible hits on more recent cases to try to nail him on those.

Westchester Deputy DA Paul Noto said Greenland is being held in Valhalla while awaiting his pre-trial hearing, set for Aug. 17, for the attempted murder of the officer.

“We’ve got him on attempted murder, so he’s looking at 25 years to life on that alone,” Nolo said. “Chances are, he’ll die in prison.”

Greenland’s lawyer, Judith Permutt, declined to comment.

Additional reporting by Shawn Cohen and Max Jaeger