Roughly 1,000 people have signed a petition to get city officials to do something about a woman they say spits, yells and chases after people on the Upper East Side. View Full Caption Facebook/Spitting Lady of the Upper East Side: Forum for Spottings

YORKVILLE — Upper East Siders fed up with a woman they say chases and spits on passers-by launched a petition demanding local politicians and Mayor Bill de Blasio "take action" — but one politician says solving the problem isn't so simple.

The woman, who officials believe is homeless, has been spitting, screaming at and chasing people between 74th and 82nd streets for years, locals said, but she's recently gotten more attention after neighbors started a Facebook forum to track her whereabouts.

The petition, which was posted last week and has gathered more than 1,000 signatures, asks officials to "take action on this, as the Upper East Side is becoming a dangerous place to walk around, out of fear this woman will assault pedestrians."

The person that created the petition posted it with the intent of sending the signatures and a letter to City Councilmen Ben Kallos and Dan Garodnick, as well as Mayor de Blasio.

"This woman is not only a nuisance, but she is a threat as she is assaulting people vilely with saliva," the petition reads. "She mainly spits on children, while also hissing and yelling at them. The community is tired of nothing being done."

People who have signed the petition say the woman terrifies locals.

"The sheer look of terror in kids' faces when she's screaming at the top of her lungs is horrifying," Upper East Sider Amy Silberman wrote.

"My wife and young children have had to literally run and duck into a store to avoid this woman's aggression; our four-year-old son was scared to go outside for a few days following one particular incident," Justin Santana added.

While local politicians said they understand the fear the woman is causing, they claimed their hands are tied until police have a reason to arrest her.

Kallos, who was one of several politicians to create the Eastside Taskforce for Homeless Outreach and Services (ETHOS) last year, said that until the woman is proven to be a harm to herself or others, he can't do anything about her.

"She's been brought to the hospital on numerous occasions and assessed by a psychiatrist," he told DNAinfo New York on Tuesday. "If anyone has been spat on, touched without consent, chased, or threatened, I will go with them personally to the 19th Precinct to swear out a complaint so that the city has additional resources to help her."

Kallos said he's successfully helped connect homeless New Yorkers with services in the past, and even sat down with the Department of Homeless Services last October to go through a list of local homeless people one by one to see what kind of services they needed.

"We've had success in some places, but there are some folks we haven't seen recently because people have accepted help, or found help on their own," he said. "The worst case is that they just disappear and we don't know what happened to them."

Kallos noted that the Upper East Side is very dense, so when there is one person singing or screaming, it's bound to impact thousands of people and amplify the the problem.

"We have been putting immense pressure on this administration to address the homeless concerns in this community and we have asked them to use every tool [they have]," he said.

► READ: Women and Children's Homeless Shelter Welcome on the UES, Pols Say

Department of Homeless Services spokesman Isaac McGinn said the agency's teams have reached out to offer services and are working with the NYPD and Kallos's office to monitor the situation.

"It can take anywhere from one dozen to more than two hundred contacts to bring street homeless New Yorkers indoors — and we are undeterred in our efforts to engage clients proactively and aggressively until we make the connection that will help them transition off the streets," he said.

The NYPD said in a statement on Tuesday that it is working with a local community organization and DHS to find housing for the woman.