Crosby has a younger sister named Taylor who is a hockey goaltender. Like her brother, she went to high school at Shattuck-Saint Mary's in Faribault, Minnesota to play with the school's hockey program. In 2014, Taylor joined the Northeastern Huskies women's ice hockey team as a freshman at Northeastern University in Boston. In 2015, she transferred to Minnesota's St. Cloud State University and played with the St. Cloud State Huskies women's ice hockey team through to graduation at the end of the 2017–18 school year.