(CNN) Amber Guyger's trial sparked protests over policing, but what happened after is now raising complaints over the US Constitution's separation of church and state.

The Freedom From Religion Foundation filed a complaint Thursday against Judge Tammy Kemp for giving the woman convicted of killing her neighbor a Bible while in the courtroom. The foundation said Kemp's "proselytizing actions overstepped judicial authority" and has asked the Texas State Commission on Judicial Conduct to investigate.

Former Dallas police officer Guyger was sentenced to 10 years in prison -- a sentence many have called inadequate -- for the murder of Botham Jean, whom she says she fatally shot after she entered his apartment thinking it was her own. At the end of the emotionally charged trial, Kemp gave Guyger a hug and a Bible.

"You can have mine. I have three or four more at home," she said. "This is the one I use every day. This is your job for the next month. It says right here. John 3:16. And this is where you start. 'For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have eternal life ...'"

While it is acceptable for Kemp to express her faith as a private citizen, the complaint argues, she was representing the US government at the time.

Read More