I didn’t do it

A woman’s body lays lifeless on the side of the bed. You didn’t kill her. She matches the description of a missing woman who made the headlines a day ago. You only went out for a walk, and it was only an hour. There was no one with you so you don’t have a strong alibi. Suddenly you hear a knock on the door. There’s two stern cops with a warrant to search your house.

How do you get out of this situation? How do you prove your innocence?