The incident took place around 12:30 p.m. Thursday at the Weed Memorial Library on Hope Street in Wingdale, said Stamford Police Sgt. Brian Butler.
According to Bulter, the man, described as being a black male in his mid-30s, with a medium build and short hair and facial stubble, walked up to the check-out desk and asked to apply for a library card. When he couldn't provide any identification, the librarian told him she couldn't provide him with a card.
The man, who was wearing a green zip-up sweatshirt and gray sweatpants, then asked where he could find books by James Patterson, Butler said.
When the librarian looked up to direct him to the books, the man had pulled down his pants and exposed his penis, Butler added.
The librarian screamed and told the man to leave the building. The man then apologized and left, Butler said.
Officers searched the area but were unable to locate him. Butler said the library's video surveillance system was down at the time.
Anyone with information is asked to contact the Stamford Police Department at 203-977-4958.
Click here to follow Daily Voice Norwalk and receive free news updates.