No sheriff, deputy sheriff, constable, city marshal, chief of police or other police officer who receives a salary or who is to be otherwise compensated as a law enforcement officer in connection with the same criminal case by the state, county, city or town shall be paid any fee for testifying as a witness in a criminal case, except that any police officer who is on vacation, furlough or on time off who attends as a witness in a criminal case pending in any municipal, district or superior court shall, upon order of the court, be paid a witness fee in accordance with N.H. Rev. Stat. § 592-A:12 for each day of such attendance; provided, however, towns and cities may pay supplemental witness fees if deemed desirable.