Is district court capitalized

"District court" is capitalized when it is used in the name of a specific court. "The Alberman case was decided by the United States District Court for the Southern District of Ohio." or "Judge Samuels was appointed to the Dayton District Court in 2005"

If the term does not refer to a specific district court, it would not be capitalized. "A civil action is commenced by filing a complaint in the district court."