(b) Subject to the conditions and limitations provided for in this subdivision, a refund or credit shall be allowed for a tax paid pursuant to subdivision (a) and paragraph three of subdivision (c) of section eleven hundred five or section eleven hundred ten of this article and any tax imposed pursuant to the authority of article twenty-nine of this chapter on the sale to or use by an omnibus carrier described in this subdivision of any omnibus, and of parts, equipment, lubricants, motor fuel, diesel motor fuel, maintenance, servicing or repair purchased and used in the operation of any such omnibus by such carrier or on the sale to or use by a vessel operator described in this subdivision of a vessel with a seating capacity of more than twenty passengers used for the transportation on water of passengers for hire, and of parts, equipment, lubricants, diesel motor fuel, maintenance, servicing or repair purchased and used in the operation of any such vessel by such operator. Any such omnibus carrier or vessel operator must provide local transit service in this state and operate pursuant to a certificate of public convenience and necessity issued by the commissioner of transportation of this state or by a like officer or agency of the United States or pursuant to the contract, franchise or consent between such carrier or operator and a city having a population of more than one million inhabitants, or any agency of such city. The amount of such refund or credit shall be determined by first computing the local transit service percentage which shall be the proportion that, in the case of such a carrier, such carrier's vehicle mileage or, in the case of such an operator, such operator's vessel hours in local transit service in this state in the calendar year immediately preceding the end of the quarterly return period, prescribed by section eleven hundred thirty-six of this article, to which such refund or credit relates bears to such carrier's total mileage operated in this state in such year or such operator's total hours operated in this state in such year, as the case may be. An omnibus carrier or vessel operator which was not engaged in local transit service in the preceding calendar year shall determine such percentage with respect to its first four quarterly returns filed pursuant to section eleven hundred thirty-six of this article, by using the proportion that such carrier's vehicle mileage or such operator's vessel hours in local transit service in this state in the first three months of such operation bears to such carrier's total mileage or such operator's total hours operated in this state in such period. The amount of the refund or credit allowable on the combined state and local tax paid on such purchases or uses then shall be determined in accordance with the following table: If the local transit service The refund or credit is: percentage is: Less than 10 percent None 10 percent 10 percent of such combined tax Greater than 10 percent but less 10 percent plus (the product of than 70 percent 1.5 times each whole percent in excess of 10 percent) of such combined tax 70 percent or more 100 percent of such combined tax For purposes of this subdivision, local transit service, vehicle mileage, vessel hours, total mileage operated and total hours operated shall be defined by rule or regulation of the commissioner and records satisfactory to the commissioner shall be maintained by the carrier or operator. An application for a refund or credit pursuant to this subdivision must be filed with the commissioner within the time provided by subdivision (a) of section eleven hundred thirty-nine of this article. Such application shall be in such form as the commissioner may prescribe. Where an application for credit has been filed, the applicant may immediately take such credit on the return which is due coincident with or immediately subsequent to the time that the applicant files the application for credit. However, the taking of the credit on the return shall be deemed to be part of the application for credit and shall be subject to the provisions in respect to applications for credit in section eleven hundred thirty-nine of this article as provided in subdivision (e) of such section.