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Police and mathematics
Because A said A didn't steal, B said A stole, and only one of them was telling the truth.

Assuming that A is telling the truth, then if B lies, it may not be stolen by A, if C lies, it may be stolen by C, and if D lies, it may not be stolen by B. So we can know that C is a thief.

Assuming that B is telling the truth, then the lies told by the other three people, A can steal, C can steal and D can't steal B, then we can know that A and C are thieves, which is impossible.

So answer C is a thief.