OAKLAND (CBS SF) — As more stories of creepy clowns continued to surface across the country, two Bay Area school districts on Tuesday were addressing clown-related threats that were made against several schools on social media.

On Tuesday afternoon, the Oakland Unified School District issued a bulletin regarding “creepy clown” messages on social media that had threatened violence and, in some cases, referenced specific schools in the district.

READ MORE: UPDATE: Woman Accused of Starting Fawn Fire Was Boiling Bear Urine to Drink

The bulletin stated that all of the messages had been shared with district police and Oakland law enforcement to investigate. The bulletin said that, while authorities generally believe the threats received by schools across the country are hoaxes, that “OUSD police and staff will be extra-vigilant.”

“The security of our students and staff is our top priority. We will be monitoring the situation closely and providing extra patrols to the schools named in the rumors and all schools in general,” said OUSD Police Chief Jeff Godown.

Meanwhile in Fairfield early Monday evening, a recently added Twitter account with the user name @clownganng1 posted a tweet that specifically mentioned both Grange Middle School and Fairfield High School.

A later tweet said “yall just really wanna die but i got yall, ill keep you updated on dates and schools,” while another singled out Rodriguez High School and Public Safety Academy High School for a visit Wednesday.

School district officials contacted the Fairfield Police Department at about 7:45 p.m. Monday evening regarding the threats. Later that night, the principals for all four school sent out a letter to notify parents of the social media threat.

“The Fairfield Police Department was immediately notified and have determined there is no credible threat to our campus,” the letter read. “As a precautionary measure the Fairfield Police Department will be on campus helping to keep the campus safe.”

In a statement released Tuesday by Fairfield Police, it was noted that “online threats toward schools or other groups, even if made as a joke, can be criminal and be disruptive and harmful to students, parents and staff.”

Authorities also said that during their investigation they discovered some young people were posting responses online to the threatening posts and suggested that parents stay aware of their children’s online activity and “talk with their children to discourage them interacting with the person making the online threats.”

“Interacting with the suspect can tend to encourage more such activity, and place the children in danger,” the statement said.

READ MORE: UPDATE: Moratoriums on Canceling Fire Insurance for California Residents Only a Temporary Fix

“We take this seriously, and yet we also rely heavily on the expertise of our police department. We didn’t want to overreact and cause too much hysteria,” said Fairfield-Suisun Unified School District Superintendent Kris Corey.

The trend of disturbing incidents with creepy clowns have been occurring across the nation in recent weeks.

According authorities, people dressed in clown costumes have been at the center of dozens of hoaxes in 23 states.

The incidents have ranged from pranks to cyber threats on social media to actual physical attacks that have been violent and even fatal.

Victims reported being chased, threatened, and harassed. In Pennsylvania, a teenager was fatally stabbed by a prowler wearing a clown mask.

There have been 12 arrests nationwide, according to the New York Times.

Last week, a teen in Monterey County was arrested for making threats on social media that he planned to bomb schools in Monterey County schools in addition to going on a shooting spree “from Salinas to King City.”

According to reports authorities were able to track the threat to an IP address that led to a home in Garfield that was searched for weapons and explosives. A 17-male was arrested after admitting to the hoax.

On Tuesday morning in Washington state, a teen was arrested at gunpoint wearing a clown mask in the Tahoma High School parking lot before school started.

Meanwhile, a Connecticut school district is banning clown costumes and any “symbols of terror” during this year’s Halloween season as authorities investigate the authenticity of a number of clown-related social media posts.

New Haven Public School officials said principals and building leaders have been requested to ban the costumes until additional information is available.

This comes amid an investigation involving police into an account on the photo-sharing social media site Instagram. The account uploaded four photos showing menacing-looking clowns with captions telling several area schools to “watch out” and “wait and see” whether the alleged threats are fake.

Garth Harries, New Haven’s school superintendent, said Tuesday the posts have been disruptive to learning and to the school’s sense of security.

“There is no question that whoever is promulgating this is making threats,” said Harries. “We don’t believe there is any credible threat of violence, but they are still making people uncomfortable.”

MORE NEWS: Retailers Warn Supply Chain Delays Could Wreak Havoc On Bay Area Holiday Shopping Season

TM and © Copyright 2016 CBS Radio Inc. and its relevant subsidiaries. CBS RADIO and EYE Logo TM and Copyright 2016 CBS Broadcasting Inc. Used under license. All Rights Reserved. This material may not be published, broadcast, rewritten, or redistributed. The Associated Press contributed to this report.