MYSTERY PLUNGE

Fatal fall, then gun bust at same Bx. apt.

A woman mysteriously fell to her death from the window of a fifthfloor Bronx apartment — and cops arrested a man with a loaded pistol in the same unit shortly after, police sources said Saturday.

A resident found 43-year-old Maria Carolina Sanchez-Tiburcio (left) with bruises on her head and body in an alley on the side of the building on Grand Concourse near East 163rd Street in Concourse Village at around 3:15 p.m. Friday.

Tenant Laurance Timber, 18, who spotted the body when he returned home from a store, said, “I didn’t believe it. I thought I was tripping. I thought I was losing it.’’

He told the super, who went to the alley with four building workers. One of them called 911.

EMS medics pronounced the woman dead at the scene.

Meanwhile, police were respond- ing to a call of a home invasion robbery in the apartment, where a man named Pedro Perez lives, the sources said.

Authorities said police were unable to find any evidence of a robbery there. But cops did find Perez inside, carrying a loaded semiautomatic pistol.

Perez, 46, was arrested and charged with criminal possession of a weapon.

It’s unclear what, if any, role he played in Sanchez-Tiburcio’s death, but she had already plunged by the time cops entered Perez’s apartment, according to police sources.

Cops were trying to determine whether she accidentally fell, jumped or was pushed.

Sanchez-Tiburcio lived more than two miles away, on Davidson Avenue, sources said, adding that officers did not know why she was in Perez’s apartment.

A building maintenance worker said it appeared Sanchez-Tiburcio may have been roughed up before her death plunge.

“I saw three cuts [on her forehead]. They were open wide. She had black and blue on her head, her arms,” the worker said. “Someone beat her up.’’

A police source said Perez had blood on him.

Perez’s neighbor Jinette Ramos said he “always had different women” in his apartment.

“He would leave late at night with his bicycle and come back in the morning. Every night he was in and out. Rushing all the time.

“He would bring people with him, a lot of pretty girls,” she added.

Timber said he watched as the cops led Perez away.

“He looked like he didn’t know what was happening,” he recalled.

“Someone asked him, ‘Papi, what’s wrong?’ He just shrugged his shoulders. Calm.

“The look on his face was blank.”