Last December, as people arrested during protests related to the death of Eric Garner waited to be released from Police Headquarters in Manhattan, an officer removed a 28-year-old woman from a holding cell there.

The woman, Leighann Starkey, a doctoral student who lives in Harlem, said recently that she was escorted to a separate area where she was asked by two detectives how she knew about the demonstrations, what social media she used to keep track of them and whether she was part of a protest group. One detective, she said, asked whether she had ties to terrorists.

Another protester held that night, Christina Wilkerson, said officers told her she would not be released until she had been questioned; she stayed in custody for about 12 hours. Ms. Wilkerson, a social worker who lives in East Flatbush, Brooklyn, added that detectives asked who employed her, whether colleagues had attended the demonstrations and who had organized them.

“It started to feel like an interrogation,” Ms. Wilkerson, 30, said. “I wondered whether they would continue monitoring me.”