“No you don’t.”
Funny, I produced a COLB when applying for a passport 3 years ago and it was rejected. I had to write the state of Iowa and have them send me a valid, certified, raised state stamped version.
State Department only requires a ‘Letter of No Record’ and maybe a baptismal record or bible class record.
Right here:
http://travel.state.gov/passport/get/Secondary%20Evidence/Secondary%20Evidence_4315.html