NYC- Actress Adrienne Shelly’s hanging death in her West Village office bathroom looked like suicide. It turned out to be murder.

The stunning whodunit was cracked yesterday after cops linked a bathtub sneaker print to a teen construction worker who allegedly snapped when Shelly made a noise complaint last week, sources said.

Diego Pillco, a 19-year-old illegal immigrant who had been renovating the apartment below Shelly’s office, told cops in a chilling confession that he was afraid of getting arrested and deported, sources said.

So he followed the 40-year-old married mom of a toddler into her apartment and knocked her unconscious, sources said.

Pillco told police he panicked and staged a suicide – using a bedsheet to string up the petite actress by her neck from a shower curtain rod, sources said.

He was ultimately done in by a Reebok sneaker print he allegedly left in the native New Yorker’s bathtub, sources said.

His arrest yesterday came as a relief to Shelly’s loved ones, who refused to believe the well-regarded indie actress and director would take her own life.

“Never, never. My daughter had everything in the world to live for,” Elaine Langbaum told the Daily News. “I never for one second believed it, never for one second.”

Shelly’s husband, Andrew Ostroy – who was grilled by detectives for five hours, who pushed police to keep investigating, who even paid for a private autopsy – had only praise for the NYPD last night.

“My wife’s senseless death is devastating to me, our families and friends,” he said. “We are incredibly grateful to the New York City Police Department for their dedication, professionalism and tenacity in following up on every lead in this case.”

It was Ostroy who sounded the alarm when he arrived at Shelly’s pad last Wednesday and found the door unlocked – and then saw his wife hanging in the bathroom, police said.

Cops at first suspected suicide because there were no signs of struggle in the apartment, and no signs of trauma to the body except for a bruise over one eye.

But when they did not find a suicide note, they turned their attention to Ostroy, a thrice-married, 47-year-old marketing executive who runs a liberal blog.

Police found no evidence of an unhappy marriage.

As they kept digging, detectives paid renewed attention to a sneaker print in the tub, which investigators originally chalked up to a sloppy misstep by a crime scene responder, sources said.

Over the weekend, detectives spotted a similar print in the dust on the brown protective paper laid in the apartment directly below, where Pillco had been working, sources said. The prints matched.

Co-workers told cops that Pillco vanished shortly after his argument with Shelly. He returned with a mark on his face, they said, which he blamed on a scuffle with another employee.

Pillco, who left Ecuador and is believed to have sneaked into the U.S. via Mexico in July, spoke little English, friends and relatives said.

He was charged with second-degree murder. He said nothing as he was led from the 6th Precinct stationhouse for his arraignment. In the building on the outskirts of Brooklyn’s Park Slope, where Pillco lives in a basement hovel, a man who claimed to be his cousin insisted he could not have killed the actress.

Pillco’s boss, Luis Hernandez, agreed.

“How did he have any argument with her if they didn’t speak any English?” asked Hernandez, 51.

But Shelly’s mother-in-law, Mildred Ostroy, told The News, “This will vindicate my daughter-in-law and my son.”

“Andrew just didn’t accept what the police were telling him, and I didn’t either,” Ostroy of Wantagh, L.I., said of her son, Andrew Ostroy. “I knew in my heart it was not right.”

Ostroy and his 2-year-old daughter Sophie were sitting shiva with other relatives in his Tribeca loft, relatives said.

“She’s fine now, but she’ll soon start asking questions,” Mildred Ostroy said of her granddaughter.