to make sure that you cannot be blamed or criticized later for something.
The police were more interested in covering their asses than in finding the killer.
idiomcover your ass AmEAmE(also cover your butt)slang a rude expression, meaning to do something now to protect yourself from criticism or blame if something goes wrong in the future:I'm going to give you some advice, Danny - you have to learn to cover your ass.I knew I'd get blamed if things went wrong, so I tried to cover my butt.
Note Using 'butt' is less rude than using 'ass', but it is better to use cover your back which is not rude at all.