Reduction In Medicare Overpayment Costs Act of 1997 - Amends title XVIII (Medicare) of the Social Security Act to: (1) provide for the imposition of administrative fees for the failure of a Medicare provider to refund to the Secretary of Health and Human Services any amount by which prospective payment to the provider has exceeded actual costs by 30 percent or more (overpayment collection); and (2) require automated prepayment screening by fiscal intermediaries and carriers of a select portion of Medicare diagnoses that the Health Care Financing Administration has determined frequently result in overpayment under the program.