You've probably already read these
http://historyresearch.utah.gov/guides/adopt.htm
http://www.utcourts.gov/resources/forms/#Emancipation_of_a_Minor
You're at a point where you have to either
1. hire a Probate atty to do the Petition or pay one for a sample 'Petition' and advice from a Probate atty.
2. create your own Petition. Do it in the adoptive parent's name (who is your client). They may have to appear in court. Heck, do it in all 3's name: parents and child.
3. contact an adoption service in Utah and see if they have a sample of a previously-used form & some advice.
Look at the Utah court forms to see the layout and follow the same top portion, using the adoption case number and names. Adoptions are under Probate Court in Utah.
Note that a 'Petition For Release Of Information' will minimally need to be:
(4) The petition shall be verified (note the statement, signatures, and notarization on the forms), and contain all of the following:
(a) the name, age, and address, if any, of the child upon whose behalf the petition is brought;
(b) the names and addresses, if known to the petitioner, of both adoptive parents and any guardian of the child;
(c) a concise statement of facts, separately stated, to support the ,,, requested information. Tell the court that the adoptive parents want this information released and the adoptee also. The parents may have to appear in court. You can put in this section that the adoptive parents request that the identifying info be released to you.
The clerk can't give advice, but she has to tell you why a filing is deficient & can't be accepted for the purpose you intend.
The cheapest, quickest and least stressful method is: hire an attorney to do this.