The young women approach tourists in Times Square and pose for photos, wearing nothing but a thong and a feathered headdress, their bare breasts painted with patriotic colors in a thin simulation of a bikini top. Then they ask for a tip.

Are they performance artists?

Are they panhandlers?

And, perhaps most important, can the city move against them without violating their right to free speech?

Those are among the questions the courts may have to answer if Mayor Bill de Blasio of New York pushes ahead with plans to rein in the activities of the women and their handlers, who have come under fire from business leaders and politicians worried they are driving away tourists.

Whatever action the city takes to control the women, it will face legal challenges at every turn. Civil rights lawyers argue the women are bare-breasted panhandlers, and so they are protected, first by two state high-court rulings that made it legal to go topless and to panhandle, and then by the free-speech clauses in the state and federal constitutions.