In answering your question it depends on what type of agency and jurisdiction they have. When looking into one of the federal and some state agencies you do stand a greater chance of having to relocate for work. On the other hand in working for a local or county agency you are less likely to relocate for the job, but there is some traveling. When I was working in investigations I did a lot of traveling mostly locally rather than relocate.
If you work for a state or federal law enforcement agency, there's always that possibility. If you work for a local agency, you might get sent to a different substation on the other side of town, or your shift hours might change, but, that's about it. If you decide to leave and go work for another agency, then, you might move.