When any person convicted of an offense shall be sentenced to pay a fine or costs, or to be imprisoned in the county jail, the clerk of the court shall, as soon as may be, make out and deliver to the sheriff of the county or some officer in court, a transcript from the minutes of the court, of the conviction and sentence duly certified by such clerk, which shall be sufficient authority for the sheriff to execute such sentence, and he shall execute the same accordingly.
MCL 769.16