Kinsey was born in Lafayette, Louisiana. When she was two, her family moved to Jakarta, Indonesia, where her father worked as a drilling engineer. They lived there for twelve years, and she attended the Jakarta International School. During this time she learned the Indonesian language, which she still speaks. Her family then returned to the United States and settled in Archer City, Texas.

Kinsey studied English at Baylor University, where she was a member of the Chi Omega sorority, "took as many theatre classes as possible", and participated in the "Baylor in London" program. In a 2007 interview with the Baylor student newspaper, she discussed the influence of her years at the university:

She married Warren Lieberstein on June 18, 2000. He is the brother of Paul Lieberstein, who plays Toby Flenderson on The Office. She gave birth to their first child, Isabel Ruby Lieberstein, on May 3, 2008. Present at the hospital, was co-star and best friend Jenna Fischer.

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