Police are searching for a suspect in the rape of a woman in the stairwell of a Midtown Manhattan building late last night, police officials said.

The victim was walking down the stairs from her fourth-floor studio on East 36th Street between Madison and Fifth avenues at about 1 a.m. when she was attacked by a man wearing a black skull cap and a gray sweatshirt, police said.

After the initial assault, the rapist bound the victim and proceeded to rape her, police sources said.

The victim’s boyfriend, who shares an apartment with her, found the woman in the stairwell shortly after the assault and called the authorities, police sources said.

After spending several hours in Bellevue Hospital Center, the victim was questioned by officers in the department’s special victims unit, police sources said.

Police were investigating how the suspect broke into the building at press time yesterday, but Commissioner Raymond Kelly said the incident did not appear to fit a pattern.

As of June 10, police statistics for this year show that there have been six rape complaints in the Midtown neighborhood where the incident took place. The number of complaints has tripled compared with the same period last year.

Several employees of businesses in the building where the rape took place said they do not feel there is a police presence after 6 p.m. in the neighborhood, which is home to a slew of retail businesses.

A woman who works on the third floor of the building where the rape occurred, Jennifer Perez, 22, complained that there are no cameras in the building.

“I still have to come to work,” she said. “But now I’ll be more careful and look around.”

Calls to the owner of the building were not answered.

Zoning records indicate that the building is designated for commercial use only. However, the owner of Abe Delivery Service, a business in the building, Abraham Fofanah, said the victim and her boyfriend have resided in the building for more than two years.