In the killing last year of three Muslim students in Chapel Hill, N.C., for instance, the authorities did not bring hate crime charges against a neighbor who is charged with murdering them, despite calls from Muslims who said there were religious overtones to the violence. The police said that a parking dispute, not bigotry, may have led to the killings.

Sometimes, the evidence is more clear-cut.

“I hate ISLAM!” a former Marine named Ted Hakey Jr. wrote to a friend on Facebook after last November’s terrorist attacks in Paris. Hours later, in a drunken rampage, he fired a high-powered rifle four times into the mosque next door to his Connecticut home.

Last month, an apologetic Mr. Hakey began a six-month prison sentence after pleading guilty to a hate crime charge.

In Brooklyn, two women out walking their children in strollers were attacked this month, the police said, by a woman who screamed anti-Muslim obscenities and tried to rip off their traditional veils. And in Queens, a man was beaten in April by three strangers who shouted “ISIS, ISIS.”

In Minneapolis, a man shouting obscenities about Islam shot two Muslim men in traditional religious garb in June, the authorities said.

In St. Louis, a man was arrested in February after the police said he pointed a gun at a Muslim family shopping on his block and told them they “all should die.”

Last month, an imam in Queens and his assistant were shot and killed execution-style on the sidewalk. The authorities have charged a 35-year-old man in the attack but have not determined a motive or whether it should be treated as a hate crime.