A down-on-his-luck US Army veteran claims he’s been wrongly labeled a sex offender — and it nearly made him homeless.

Kevin Tillman, 55, was couch-surfing at a friend’s, without diabetes meds, and fell so ill his leg had to be amputated in January.

Desperate, Tillman sought help from the city Department of Housing Preservation and Development over the summer, only to be rejected when the agency said his name appeared on the state’s sex offender registry, according to court papers.

Tillman had never been arrested for a sex crime. But a relative, Jeffrey Washington, also 55, was convicted of child rape in the 1990s and once used Tillman’s name and date of birth as an alias with cops.

Tillman “was my cousin. I used his name,” Washington admitted to The Post.

The name swap caused Tillman’s name to absorb Washington’s rap sheet — landing the Army veteran on the sex-offender registry and making it appear as if he had a criminal record.

“It’s terrible. Why me?” Tillman said. “They should have known. They have my fingerprints,  they have his fingerprints.”

Tillman provided fingerprints to the NYPD in August proving his identity, and was eventually approved for an apartment in The Bronx. He’s now suing the state and the Division of Criminal Justice Services, which administers the Sex Offender Registry, for $5 million, claiming the mix-up rendered him “guilty until proven innocent.”

Tillman, who was living in Colorado when Washington was arrested on his child rape charge, doesn’t know how long his name has been listed on the perv registry.

The state needs to do a better job differentiating aliases used by sex offenders from real criminals, Tillman’s attorney said.

“What they’re doing here is blindly putting every alias up on the internet, there’s nobody making any distinction” between aliases and offender names, said lawyer Peter Traub. “You’re innocent until proven guilty — unless a sex offender uses your name.”

Tillman still appears on an undated “most wanted” list available online from the state Corrections Department. But the entry describes Washington’s tattoos, and crimes. The mistake even extended to a 2012 list from then-state Sen. Jeff Klein, who included Tillman’s name on a tally of sex offenders in homeless shelters.

Tillman does have three minor arrests on his record — one for pot possession and another related to his street vending work — both in 2008.

Washington, who was released from prison in 2011, said he didn’t have any grudge against Tillman when he used his name.

“I was scared. I didn’t know the harm it would cause,” he told The Post.

Arrested in 1991 for a child rape he still insists he didn’t do, Washington said he was out on appeal, on drugs and unable to find a job in 1994 when he snatched a woman’s purse in Downtown Manhattan. That’s when he gave cops Tillman’s information instead of his own. 

Washington claims state prison officials listed him under his cousin’s name — even though they had his fingerprints and a prior case on file and knew his real identity.

“I didn’t have anything against my cousin,” Washington said. “I regret it every day.”