Crane was born in Waterbury, Connecticut, and spent his childhood and teenaged years in Stamford. He began playing drums, and by junior high was organizing local drum and bugle parades with his neighborhood friends. He later joined his high school's marching and jazz bands and the orchestra. He played for the Connecticut and Norwalk Symphony Orchestras as part of their youth orchestra program.

In 1965, Crane was offered the starring role in a television situation comedy about a German POW camp. Hogan's Heroes became a hit and finished in the top 10 in its first year on the air. The distinctive military-style snare drum rhythm that introduces the show's theme song was played by Crane himself. The series lasted for six seasons, and Crane was nominated for an Emmy Award twice, in 1966 and 1967. In 1968, he became romantically involved with cast member Patricia Olson, who played Hilda under the stage name Sigrid Valdis. He divorced Anne in 1970, just prior to their 21st anniversary, and married Olson on the set of the show later that year. Their son, Scotty, was born June 4, 1971, and they later adopted a daughter, Ana Marie. The couple separated in 1977, but according to several family members, reconciled shortly before Crane's death. In 1968, Crane and series costars Werner Klemperer, Leon Askin, and John Banner appeared with Elke Sommer in a feature film, The Wicked Dreams of Paula Schultz, set in the divided city of Berlin during the Cold War. In 1969, Crane starred with Abby Dalton in a dinner theater production of Cactus Flower. Crane frequently videotaped and photographed his own sexual escapades. During the run of Hogan's Heroes, Richard Dawson introduced Crane to John Henry Carpenter, a regional sales manager for Sony Electronics, who often helped famous clients with their video equipment. The two men struck up a friendship and began going to bars together. Crane attracted women due to his celebrity status and introduced Carpenter as his manager. Later, they would videotape their sexual encounters. While Crane's son Robert later insisted that all of the women were aware of the videotaping and consented to it, some, according to one source, had no idea that they had been filmed until informed by Scottsdale police after Crane's murder. Carpenter later became national sales manager at Akai, and arranged his business trips to coincide with Crane's dinner-theater touring schedule so that the two could continue seducing and videotaping women after Hogan's Heroes had run its course.

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