There is. In fact there was an investigation by the Office of Civil Rights (OCR) into this very issue. Under the Health Information Portability and Accountability Act (HIPAA), a physician cannot hold a patient's medical record hostage while the patient has an outstanding balance. The link to the OCR's opinion on this is below, followed by the OCR's summary of the issue.
Private Practice Revises Access Procedure
Covered Entity: Private Practice
A [patient] alleged that a private practice physician denied her access to her medical records, because the [patient] had an outstanding balance for services the physician had provided. During OCR’s investigation, the physician confirmed that the complainant was not given access to her medical record because of the outstanding balance. OCR provided technical assistance to the physician, explaining that, in general, the Privacy Rule requires that a covered entity provide an individual access to their medical record within 30 days of a request, regardless of whether or not the individual has a balance due. Once the physician learned that he could not withhold access until payment was made, the physician provided the complainant a copy of her medical record.
Hope that helps. If the physician refuses, you are more than entitled to contact your local branch of the Office of Civil Rights, or contact an attorney to help you with the process. Let me know if I can provide any further assistance.