You will need to determine if you are eligible to change your place of birth details. You can download form DS-5504 from the U.S. Department of State website. You need to be able to truthfully check the yes box next to the statement "My identifying information in my most recent U.S. passport book and/or U.S.passport card was printed incorrectly." If this applies to you then it may be possible to change your place of birth details.
Form DS-5504 exists so that U.S. passport holders can change their information so it is accurate. It allows applicants to change incorrectly printed identifying information by entering the correct data. When applying to have your identifying information altered, you will need to supply the appropriate documents along with form DS-5504. In this case a valid birth certificate should be appropriate. You will also need to send your current passport card or passport book.
As of 2011, the U.S. Department of State no longer amend passports and issue replacements instead. You will, therefore, need to submit two recent color photographs which meet U.S. passport standards along with your application.
Anyone who knowingly submits false information or documents as part of their U.S. passport application process can be fined and/or imprisoned.