N.Y. County Law § 380
In counties which, upon the effective date of this section, operate on the basis of a fiscal year expiring prior to December thirty-first, nineteen hundred fifty, there may be included in the first tentative budget prepared pursuant to this article an amount sufficient to pay, in whole or in part, all accounts, claims and demands against the county and obligations of the county, duly audited or otherwise payable by the county for or during the period elapsing between the date upon which such fiscal year would have expired and January first, nineteen hundred fifty-one; provided, however, that a county may finance, in whole or in part, the payment of obligations and expenses falling due during such period by the issuance of serial bonds or capital notes pursuant to the local finance law.
N.Y. CountyLaw § 380