Yes, most states have in place laws that require an insurance provider to either accept medical bills related to a PIP (personal injury protection) no-fault claim within a certain period of time. Some states may only say within a "reasonable" amount of time while others have a specific time frame outlined in their laws. You did not mention your state so for an example here is information on New York States PIP claims.

The NYS Insurance Department states that in the event you are injured in a motor vehicle accident, you should file a written notice of claim with the No-Fault insurer setting forth details sufficient to identify the injured person(s), along with reasonably obtainable information regarding the time, place and circumstances of the accident, as soon as reasonably practicable, but in no event more than 30 calendar days after the date of the accident, unless you can submit written proof providing clear and reasonable justification for late filing.

Within five business days after the insurer receives this notice of claim, they are required to send you an Application for Benefits and a letter explaining the No-Fault coverage available and your rights and obligations. Once you receive the Application for Benefits form, complete and return it as soon as possible.

If you need medical treatment, you: (1) can pay the doctor or hospital directly and submit your receipts or bills to the insurer for reimbursement; or (2) may be able to assign your benefits to the doctor or hospital and have them submit their bills directly to the No-Fault insurer for direct payment, or (3) can permit the health care provider to bill the No-Fault insurer directly by providing them with a “direction to pay” for claims.

No-Fault benefits are paid in accordance with prescribed fee schedules, which the health care provider is required by law to accept as full payment. It is important that you make clear to the health care provider that you are being treated for injuries related to an auto accident. Unless additional verification is requested, the insurer is required to make payment within 30 days of receipt of your physician’s and hospital’s treatment report, or your employer’s report of earnings you have lost.

If the insurer fails to make a timely payment of a No-Fault claim, it must pay 2% interest per month on the unpaid amounts and any reasonable attorney’s fees (in accordance with Insurance Department regulations) you have incurred in order to collect your overdue No-Fault benefits.

If all or part of your No-Fault benefits are denied or paid late, you may: (1) file a complaint with the NYS Insurance Department; (2) request No-Fault arbitration; or (3) bring an action in court. No-Fault arbitration can be requested if the insurer denies your claim in whole or part, fails to make a timely payment of benefits owed, or fails to inform you in a timely manner if your claim has been denied.

NYS also has in place Insurance Department Regulation 68 which revised the no-fault and became effective April 2002.This effected numerous changes to the processing of No-Fault claims in New York. The revised Regulation modified the time frames in which to submit written notice of claim from 90 to 30 days and to submit medical bills from 180 to 45 days, respectively, and mandated that lost wage claims must be submitted within 90 days.

As a second example in Florida, another no-fault state, your insurance company must provide you with a notice of your rights when you file a PIP claim. This notice will include items such as a list of your PIP benefits, exclusions and limitations, and payment deadlines. Your insurance company must pay you or the service provider within 30 days upon receipt of proper written notification of the PIP loss amount.

To find out your specific state's laws regarding deadline for an auto insurance carrier to pay out for PIP claims contact your state's insurance regulator.