Miss. Code Ann. § 99-3-13

If a person commit an offense and be pursued by a sheriff or constable, and escape from the county of the officer, the officer may pursue and apprehend him in any county and take him to the county in which the offense was committed; and in all cases an officer or other person having the lawful custody of a prisoner, passing through any county on his route, may lodge the prisoner in any jail for safekeeping, as circumstances require. In like manner if a person commit an offense within the corporate limits of an incorporated municipality and be pursued by a marshal or any other municipal peace or police officer and shall escape from the municipality, such municipal peace or police officer may pursue and apprehend such offender to places without the corporate limits of the municipality and to any place within the State of Mississippi to which such person may flee and may return such person to the municipality in which such offense was committed.