In a proceeding pursuant to CPLR article 78 to review a determination of the Board of Zoning Appeals of the Unincorporated Village of Málveme, dated May 27, 2004, which, after a hearing, inter alia, affirmed a decision of the Building Inspector denying the petitioners’ application for a building permit, the petitioners appeal from a judgment of the Supreme Court, Nassau County (Peck, J.), dated December 13, 2004, which denied the petition and dismissed the proceeding.
Ordered that the judgment is affirmed, with costs.
Local zoning boards have broad discretion (see Matter of Pecoraro v Board of Appeals of Town of Hempstead, 2 NY3d 608, 613 [2004]; Matter of Halperin v City of New Rochelle, 24 AD3d 768, 771 [2005]), and judicial review is thus limited to determining whether the zoning board’s action was arbitrary, capricious, or an abuse of discretion (see Matter of Fuhst v Foley, 45 NY2d 441, 444 [1978]; Matter of Mangan v Cianciulli, 19 AD3d 598 [2005]).
Here, the denial by the respondent Board of Zoning Appeals of the Unincorporated Village of Malverne (hereinafter the Board) of the petitioners’ application for a building permit on the ground that the proposed use was not permitted in the residential districts in which the property was located had a rational *853basis in the record and was not arbitrary or capricious (see Matter of Ifrah v Utschig, 98 NY2d 304, 308-309 [2002]; Matter of Sasso v Osgood, 86 NY2d 374, 384 [1995]; Matter of Taggart v Tortora, 24 AD3d 456, 457 [2005]). The petitioners failed to establish that the proposed propane filling station was an accessory use to the permitted nursery/garden center. Thus, the Supreme Court properly declined to disturb the Board’s determination (see Matter of Pecoraro v Board of Appeals of Town of Hempstead, supra at 614-615; Matter of Blake v Planning Bd. of Town of Philipstown, 21 AD3d 486, 487 [2005]).
The petitioners’ remaining contention is without merit. Crane, J.P., Ritter, Krausman and Spolzino, JJ., concur.