Women in Grozny, the capital of the predominantly Muslim region of Chechnya, said on Friday that several times this month the police had fired paintball pellets at them for not wearing head scarves. The attacks, which outraged activists, highlight tension over efforts by Chechnya’s Moscow-backed leader, Ramzan Kadyrov, to enforce Muslim-inspired rules that in some cases violate Russia’s Constitution. A spokesman for the Interior Ministry, which handles the police force, would not comment. Critics say that in return for keeping relative calm in Chechnya, the site of two separatist wars with Moscow since the mid-1990s, the Kremlin allows Mr. Kadyrov to run it like a personal fiefdom and lets him impose his vision of Islam, which includes periodic bans on alcohol and making women cover their heads in state buildings.