on someone’s case—
1. investigating smb.’s crime:
- He has been able to avoid getting caught by every other detective on his case.
2. (U.S. sl.) harassing or criticizing a person in an annoying way:
- “My sister was on my case about that joke all night,” he continued.
on the case—
1. = on someone’s case 1:
- The detectives on the case think the two things are tied in. The killing and the acid.
2. dealing with a particular problem or situation:
- The missions seem designed only as a chance for politicians to show they’re on the case.