NEW YORK – After three rounds of interviews, Sarah De Stefano felt good about her prospects of landing her first job as a lawyer — until she hesitated when told to add a background-check investigator as a Facebook friend.

He’d seen her sparse public page and wanted to go through the pictures and posts she shared only with friends and relatives. She felt the request invaded her privacy, said no and eventually got a rejection letter from the employer, an upstate New York government legal agency she won’t name.

“I, honestly, have nothing to hide, no embarrassing pictures or extreme Facebook posts, but I still just didn’t feel comfortable with it,” De Stefano told city lawmakers Wednesday as they discussed a proposal to bar employers from demanding a look at job-seekers’ private lives on social media.

The plan would extend a new wave in digital-privacy laws to the nation’s biggest city.

In the last two years, 14 states have passed laws barring employers from demanding that prospective hires and/or current employees allow access to their non-public postings on social sites, according to the National Conference of State Legislatures. New York state and more than 20 other states have been considering similar measures.

New York Civil Liberties Union lawyer Nate Vogel said if New York City joined the list of governments that are passing such legislation, “that would send a really powerful signal.”

City Councilwoman Annabel Palma’s proposal would generally prevent companies from asking applicants and current workers to provide passwords, accept friend requests or change privacy settings so the employer could see social media postings and email that the general public can’t.

Violations could lead to city fines, and workers could sue employers. Companies still could scour an applicant’s public postings, monitor personal use of work computers and request access to personal online accounts to investigate misconduct allegations.

The measure’s supporters note that job applicants may post to their friends and family about health, religious and other personal matters about which companies cannot legally ask.