baby passport question

I feel really stupid for asking this but are we supposed to sign our baby's US passport?  I received my 3 month old's US passport in the post a few weeks ago (following the consular appointment).  We are flying this week to the US and when I had a look at the passport I was wondering if I should leave it blank till he can sign it or sign it for him.  His British passport states clearly not to sign but I don't have any instructions about the US one.      Couldn't find any info on the passport site.

I know its a silly question but I'm flying into Philly and I know the immigration guys there can be a bit ridiculous at times.  I had a bad experience there once that I don't want to repeat.

Thanks.

At the embassy they told me to sign my name, and behind my name write something like (Parent/Guardian of *baby's full name*) - He's used his passpoert loads and we've had no problems.