In order for NYPD to effectuate an arrest all that is needed is a complaint alleging a crime, this may be wholly based on circumstantial evidence - meaning there is no physical evidence outside of the person filing the complaints word.
Generally the Police will do some further investigation into the allegations, in most cases minor, and then follow through with an arrest.
He said she said....
YES, a single persons word IS enough to make a complaint valid and enough cause to arrest an individual. However, all complainants MUST also later sign a corroborating statement with the DA and appear in court as witnesses... if these two do not happen the case must properly be dismissed in court against you after the constitutional speedy trial period has passed