Where, in proceedings in a Court of a State or Territory, a claim is made against the Commonwealth or a Commonwealth authority for damages in respect of the death of, or personal injury to, a person caused by, or arising out of the use of, an uninsured motor vehicle, the question whether the claim shall be tried with or without a jury is to be determined in accordance with the law that would be applicable, in proceedings in that Court, in the case of a like claim against the owner of a vehicle in respect of which there was in force a third - party policy effected for the purposes of, and in accordance with the requirements of, the law of that State or Territory.