Harish stole the monkey, Manoj stole the cat and Tarun, the dog.

Explanation: The statements and known facts are:

Harish: Tarun stole the cat.                                 — S1
Manoj: Tarun stole the dog.                                — S2
Tarun: I didn’t steal the cat or the  dog.        — S3

Facts:
The one who stole the monkey told a lie  — F1
The one who stole the cat told a truth       — F2

Statement 3 (by Tarun) says that he didn’t steal the cat or the dog. If we assume that this statement was true, it implies that he stole the monkey. However, as per the known fact F1, (person who stole the monkey lied), the statement S3 must be false, contradicting our assumption. This, in turn, implies that Tarun stole either the cat or the dog. However, had he stolen the cat, he would have told the truth (as per the known fact F2). Thus, the only possibility is that Tarun stole the Dog.

Now, what remains is to identify who stole the cat and the monkey. We know that one of the remaining suspects (who took the monkey) told a lie and the other (who took the cat) told the truth. Had Harish told the truth (S1), Tarun should have taken the cat. However, we know that Tarun did not take the cat. (He took the dog.) So, what Harsh told was a lie, whereas Manoj had said that Tarun stole the dog, which turned out true. This implies that Harish stole the Monkey (and lied, as per fact F1) and Manoj stole the cat (and told the truth that Tarun stole the dog.).