Wow--a lot of responses to this one. Thanks everyone.
Listen, I'm no moron. I know I had the right to refuse a search of my house, but quite frankly, I thought, "if my kid stole something, then he's gotta pay the price". I'd rather him learn his lesson NOW while I'm still able to guide him.
The officers were just doing their job, they were polite and answered any questions I had. Im sure my dorky son walking around at 11:30pm after curfew (to break in his new shoes that he just took out of the MICROWAVE!) looked rather suspicious, especially when some kids have been breaking into cars in the neighborhood recently.
With that said, if officers came to do a search on my house for a very serious matter and I had any reason to think they'd find something that would pose questions, I would most certainly consider refusing the search at that moment.