The following persons who are financially unable to obtain counsel shall be entitled to be represented by a judicial district public defender:

(1) A person charged with a felony, including appeals from convictions for a felony;

(2) A person pursuing a postconviction proceeding under sections 29-3001 to 29-3004 after conviction of a felony, when the public defender after investigation concludes that there may be merit to such a proceeding or when the court in which such proceeding is pending directs the public defender to represent the person;

(3) A minor brought before the juvenile court when neither the minor nor his or her parent or guardian is able to afford counsel; and

(4) A person against whom a petition has been filed with a mental health board as provided in sections 71-945 to 71-947.