When police question you in connection with a crime, it is often in your best interest to remain silent. In fact, when police ask where you were at X time and on X day, both a weak and strong alibi can hurt you. Talk with an attorney before answering any questions, including alibi questions. For example, if your alibi is strong and easy to verify, you do no harm by consulting with an attorney first. You can always offer your alibi to police later if it is that easy to verify.
What if your alibi is weak, though? Will it be hard to overcome?