Crosby was born in Hollywood, California, the daughter of Marilyn Scott and actor Dennis Crosby. Her paternal grandfather was actor/singer/comedian Bing Crosby. She attended LeConte Junior High School with actress Rita Wilson (wife of Tom Hanks).  Her choice of career solidified at an early age and was influenced by the involvement of other family members in show business.
Crosby was married to Geoffrey Edwards (son of director Blake Edwards) from 1983 to 1990. She appeared in a few of Blake Edwards' films, including Skin Deep, Trail of the Pink Panther, and Curse of the Pink Panther.
Crosby is currently married to Ken Sylk. They have a son, August William Sylk.