CRANSTON, R.I. — A dispute over women’s place in the Santa Maria di Prata Society has escalated from arguments over access to the organization’s lounge to police involvement, a no-trespass order and the threat of a lawsuit. The conflict came into focus recently when women arrived at the society for their regular Tuesday card games and bocce and found the lounge locked. Male members were inside, and society President Anthony Mastantuono said the women would have to prove they belonged to the Women’s Auxiliary before entering. Members of the auxiliary are seeking equal standing in the Italian American organization. The standoff has drawn a sharp line between women pressing for a greater role and a society whose practices reflect longstanding gender divisions. Stephanie Giarrusso, the auxiliary’s vice president, is subject to a no-trespass order filed by Mastantuono. The dispute has also involved police and the possibility of legal action, though no lawsuit is identified as having been filed. The confrontation touches the society’s everyday community life as well as its governance: the lounge is a gathering place for members, and the Tuesday activities bring women together at the Cranston organization. The conflict raises questions about who gets access to shared spaces and whether the auxiliary’s members will have an equal voice in the society.