Cross-dressing killer ​multimillionaire ​Robert Durst turned himself in to Houston cops to face a charge that he ​exposed himself and then ​ ​urinated on a cash register and candy counter at a CVS near his upscale condo, police said Thursday.

The New York real estate heir ​was freed on a $5,000 bond after being charged with criminal mischief for the bizarre incident, which took place Sunday about 12:15 p.m. after he had calmly walked into the store and picked up a prescription.

The 71-year-old declined comment after he was released Wednesday evening.

​In 2001, Durst was busted as a fugitive and admitted killing his neighbor and dumping the remains in Galveston Bay. He claimed self-defense and beat a homicide rap.

Durst was also ​the only suspect in the 1982 disappearance of his first wife, Kathleen McCormack, a medical student who vanished after meeting Durst at their home in Westchester.​

Durst has been cut off from his wealthy family — which runs The Durst Organization, a privately held billion-dollar real-estate company that owns several New York skyscrapers.

Last year, he was arrested for trespassing on his brother Douglas’ property at 413 W. 43rd St. — and 13 family members have taken out restraining orders against him.

Durst remains free on bail in the trespassing case, and is due back in court Sept. 22.

But Manhattan Supreme Court Judge Jill Konviser is likely to move that date up given the Houston charge, and could remand Durst or hike his bail.

Last week, The Post reported that he sold two Brooklyn properties for $21.15 million, more than doubling his initial investment.