SAN LEANDRO — An East Oakland street gang has threatened and may have been stalking San Leandro police after officers shot and killed a woman there in December, authorities said Thursday.

In the days and weeks after the shooting, two officers have reported being tailed by suspicious persons to their homes in San Ramon and Livermore, as part of a series of suspicious instances putting the department on higher alert, officials said.

Police do not know if those instances and others are related to the threats, but the gang’s threats pertained to police shooting and killing 27-year-old Guadalupe Manzo Ochoa after she allegedly tried to ram officers with her car on Dec. 7. San Leandro police tried to pull Ochoa over for being in a stolen car, but she drove off, leading police on a chase that ended in an East Oakland cul-de-sac in the 9800 block of Springfield Street.

Lt. Robert McManus of San Leandro police said Thursday the threats by the gang were deemed credible by police investigators gathering intelligence in East Oakland.

The names of the officers have not been released, as several investigations into the shooting are open, so the threats were “almost like a blanket statement of San Leandro police officers in general,” McManus said.

It first began hours after officers shot Ochoa, when San Leandro officers returning to the shooting scene were nearly run off the road by another driver. Oakland police later found the abandoned car, which earlier had been reported stolen.

Then, at about 11 p.m. on Dec. 11, a San Leandro police officer said he was tailed to his Livermore home by a car with four men inside, McManus said. The men — who were dressed in the manner known to East Oakland gang members, McManus said — got out and approached the officer, who was in his personal car and not in uniform, but when the officer confronted them they ran to the car and drove off, escaping after he gave chase.

In February, another officer reported being followed to his home in San Ramon, hours after a San Leandro gang member allegedly fired a gun outside a bar where the California Highway Patrol was conducting a DUI stop, McManus said.

In two other recent instances, off-duty detectives have been confronted by suspects they were investigating for violent crimes, McManus.

“We do not know if any of these incidents are connected,” McManus said. “It’s raised our awareness that police officers are really cops 24 hours a day. Whether you are on duty or off duty, people recognize who you are.”

David DeBolt covers breaking news. Contact him at 510-208-6453. Follow him at Twitter.com/daviddebolt.