When authorized to do so by the sheriff, a constable of a justice of the peace court, or a constable or marshal of a city court, within the territorial jurisdiction of his court, may serve any process and execute any writ or mandate which the sheriff is authorized to serve or execute.

For such purpose, the constable or marshal possesses the powers and authority of the sheriff; a service or execution so made has the same effect as if made by the sheriff; and the latter is responsible for the performance or nonperformance of his duties by a constable or marshal in such cases.