You may need to drag out the support worksheets.

Do as Lisa says, you need to work the numbers to see if the child provides more than half of his support.  You'll need that documentation for your files to justify the position taken on the return.

 I don't believe he contributes much to the household bills ; maybe groceries and a water bill.

"I don't believe" isn't exactly meeting the professional standard needed to sign that jurat on a tax return.