Parton was raised in the Church of God. She is the youngest of twelve children born to Avie Lee Caroline (née Owens; 1923 – 2003) and Robert Lee Parton Sr. (1921 – 2000). Her Celebrity siblings include entertainer Dolly Parton, as well as Randy and Stella Parton.

In 1982, Dennison landed her first and only acting role in the ABC television sitcom incarnation of 9 to 5. Before the show premiered, she stated in a People magazine interview: "I'm sure people will compare me to Dolly—it's only human nature." Her role, as bombshell secretary Doralee Rhodes, had been originated by her older sister, Dolly Parton, in the hit 1980 theatrical film of the same name. 9 to 5 was shot before a live studio audience and co-starred Rita Moreno and Valerie Curtin. The series had an impressive beginning in the ratings, but after a retooling (including the addition of Leah Ayres to the cast), the series was canceled by ABC after 33 episodes in 1983. The sitcom proved popular in reruns, leading producers to revive it in first-run syndication in 1986. Sally Struthers joined the cast, and the sitcom's popularity revived, producing another 52 episodes before ending in 1988.

Dennison never acted again after 9 to 5 was canceled in 1988. During the network run of the series, she and her fellow cast members appeared on an episode of Battle of the Network Stars in 1983. She performed alongside her sister in a 1987 episode of her sister's variety series Dolly. Dennison's last appearance on camera was during an episode of Bravo Profiles titled "Dolly Parton: Diamond in a Rhinestone World" in 1999. Dennison has since retired from acting and singing.