Legal Question in Criminal Law in Tennessee

Yes, it happens all the time. Often the defendant is in custody (jail or Tennessee Department of Corrections). The usual procedure is for the defendant to file a short "skelton" petition, the trial judge looks at it, and if there is a "colorable claim" (reasonable basis) to believe the petition is justified, the judge appoints either the public defender or a member of the private bar to file any amendments needed and then argue the petition at a hearing.

The biggest single reason the pubic defender would NOT be appointed is if the defendant is alleging ineffective assistance of counsel, and his attorney at trial was a public defender.