Julio Mario Galeano, an East Hampton Village police officer who allegedly used a house on Talmage Lane in East Hampton for a romantic encounter with a female member of the department in December without the permission of the house’s owner, will resign from the department effective Aug. 2. Terms of his resignation are subject to ratification by the East Hampton Village Board, according to a statement issued Monday by Rebecca Molinaro, the village administrator. On Tuesday, Mayor Paul F. Rickenbach Jr.