The family’s wealth could help distance her from the corruption investigations swirling around the department and City Hall, said Jillian Snider, a lecturer at John Jay College of Criminal Justice and a former New York police officer.

“It would be fair to say someone who comes from that level of wealth would be less susceptible to temptation,” she said. In all Ms. Tisch’s years in government, “there’s been no scandal,” Ms. Snider said. “There’s been no corruption or even the perception of something corrupt in her background that I know of…”

Ms. Tisch’s biggest obstacle as she returns could be that she never served in uniform, said Ms. Snider, the lecturer.

She said officers might not feel confident if “their top executor does not know the job that they do every day.”

But someone with a deep background in management and organizing could be more beneficial to the department now than someone who has walked a beat, Ms. Snider said.