While on a patrol an OPFAC comes upon a vessel which has run aground. After assessing the risk to both vessels may the facility be used to tow the stranded vessel back into safe water?

If the vessel is still aground this is considered salvage and the tow must be authorized by your OIA. If the vessel is afloat then the standard rules apply for a vessel in need of assistance.

From the Operations Policy Manual, COMDINST 16798.3E, page 4-22

Always check your standing orders from your OIA.

E.9.a. Requests for Assistance
 When an Auxiliary vessel on routine patrol or otherwise on orders discovers a vessel requesting assistance, but is not in contact with the Coast Guard, the Auxiliarist will relay the request for assistance to the Coast Guard Operational Commander and may undertake to provide assistance, if capable.
 
E.9.b. Safety Considerations
 If a tow is undertaken, the Auxiliary vessel is required to notify the Operational Commander of the identity of the vessel, location of the vessel, and the destination to which the vessel is being towed. No Auxiliary vessel may undertake the tow of another vessel unless the coxswain is reasonably assured of the safety of both vessels and the persons aboard. If the Auxiliary vessel cannot safely tow a disabled vessel that is standing into danger, it may endeavor to remove the persons from the threatened vessel and stand by until a more capable resource arrives on scene.

In cases involving towing by the Coast Guard Auxiliary, the vessel being assisted will normally be taken to the nearest safe haven. Coast Guard Auxiliary resources should not tow the vessel beyond the nearest safe haven when there are commercial resources that could perform this function. Exceptions to this policy may be made in specific cases if, in the judgment of the SAR mission coordinator (SMC), they are warranted by humanitarian or other concerns.
 
E.9.c. Non-Emergency Assistance
 In cases involving towing by the Coast Guard Auxiliary where no emergency exists, the assisted vessel may be released to another provider who appears capable provided that;

• The SMC and coxswain of the assisting vessel determine that a hand-off can be carried out safety, and either Alternative assistance is desired and arranged by the operator of the vessel being assisted; or The Operational Commander has a higher need for the Auxiliary resource.
 
E.9.d. Commercial Assistance
 In cases when a Coast Guard Auxiliary facility under orders arrives on scene nearly simultaneously with a commercial provider, the Auxiliary coxswain should report to the SMC, remain on scene until it is confirmed the provider is capable of providing the required assistance and safely completing the case and the disabled vessel owner/ coxswain accepts the assistance; then clear the area and take no further part in the incident.

When a mariner requesting assistance rejects the first arriving commercial assistance, Coast Guard or Coast Guard Auxiliary units should not assist in these cases so long as the situation remains classified below the DISTRESS phase (see

U.S. Coast Guard Addendum to the United States National Search and Rescue Supplement (NSS) to the International Aeronautical and Maritime Search and Rescue Manual (IAMSAR), COMDTINST M16130.2 (series)).