Annabell Randolph lost her job two years ago when she asked her boss if she could take two days off of work — one day to get an order of protection against her boyfriend, who had been beating her, and the other to move into an emergency shelter.

She took the days, and the pink slip, and moved into a shelter, but she warns now, “When you don’t have a job to go back to, a lot of women go back to their batterers.”

In an effort to prevent those situations, two Brooklyn City Council members last week each introduced a bill that tries to strengthen protections for domestic violence survivors both in their homes and on the job.

Bloomberg administration officials argue, however, that both pieces of legislation could make matters worse.

Councilmember David Yassky’s bill moves to expand an existing law that protects domestic violence victims like Randolph from discrimination in the workplace. The current law prohibits businesses from firing an employee or denying her a job because she has been abused, but, says Yassky, it does not go far enough. The new bill would expand those protections to include housing situations, and would extend those rights to victims of sexual abuse and stalking, as well. An employer might have to allow a worker to take time off to go to court, and a landlord might have to allow a tenant to change the locks on her apartment.

This proposal has not gone over well with the Bloomberg administration. Because the bill excuses battered women from having to present evidence, like a police report, before receiving these protections, “It would not only make it difficult to determine whether the individual required accommodation by an employee or landlord,” said Yolanda Jimenez, commissioner of the Mayor’s Office to Combat Domestic Violence. “It also flies in the face of efforts to encourage victims to report crimes of domestic violence to the police.”

The city found the second bill, introduced by Councilmember Bill deBlasio, unnecessary altogether. His legislation would prohibit the city’s domestic violence shelters from requiring proof of domestic abuse, like a police report, before admitting a client.

While the New York state social service law says the only criteria for entering a shelter is a signed statement attesting to being abused, advocates for abuse victims say some of their clients have been turned away because they did not have a police report. Laurel Tumarkin of HELP USA says about 40 percent of the group’s clients who live in regular homeless shelters are victims of domestic violence.

This bill, said deBlasio, would clarify the state law. “We first need to protect the victim and the victim’s family,” said deBlasio, “and worry about legality second.”