As well, two complaints of cyber bullying were made to Oamaru police in the same day.
On Monday, a 14 year-old girl claimed that a 28 year-old man had been sending her threats on Facebook, and the same day a 23-year-old woman told Oamaru police she had received an offensive text message.
Sergeant Wayne Brew said the nature of the alleged threats in both cases had not been established, but inquiries would continue.
Sgt Brew added that if unwanted comments received through social media or text messages involved threats of a physical nature or comments of a graphic sexual nature, then people should contact the police.
''There are certain things we can do; we can actually approach Facebook to find out who that particular user is, and where they are registered, and obviously if they are in New Zealand we can deal with them under the Criminal Harassment Act.
"There are a number of statutes we can actually deal with them under, depending on what they have said.''
Threats or unwanted messages should ''never'' be responded to directly, he said.
Representatives from schools in Oamaru yesterday said cyber bullying was rare in the town, but welcomed proposals put forward in the Harmful Digital Communications Bill, which would make it an offence to send messages and post material online with intent to cause harm - an offence that could be punishable by up to three months' imprisonment or a $2000 fine.
The Bill received its first reading in Parliament yesterday.
Waitaki Girls' High School (WGHS) assistant principal Glenn Potter said the school was ''very supportive'' of the heavier penalties proposed in the legislation.
Similarly to other schools, WGHS had needed to deal with ''some inappropriate issues around digital technology'', which had been responded to ''appropriately''.
''One of the key ways WGHS deals with inappropriate use of digital technology is through providing appropriate education to our girls.
''This year, WGHS and Oamaru Intermediate School were instrumental in bringing down a Netsafe representative to talk to the North Otago community [parents and pupils] about current issues surrounding safe use of technology.''
However, technology could not be hidden in an educational setting and it was important for schools to educate pupils about the recent headlines so they could make ''wise and appropriate choices for themselves when necessary'', he said.
Oamaru Intermediate School deputy principal Deidre Senior said any move supporting victims of cyber bullying was positive.
The school did not have much trouble with cyber bullying, but followed through on anything it heard, she said.
''It's OK to actually go and tell somebody; you don't have to put up with it.''
The pupils were encouraged to tell a trusted adult if they were being bullied, Mrs Senior said.
St Kevin's College deputy principal Kerry Ryan said the Bill's proposals were ''a great idea''.
Cyber bullying was not a common occurrence but could occur, he said.
The school ensured pupils could talk to senior pupils and staff if there was a problem.
''We provide them with lots and lots of opportunities to get someone on their side,'' Mr Ryan said.
The new Bill would also make a new offence of incitement to commit suicide, even in situations when a person did not attempt to take their own life, punishable by up to three years' imprisonment.
- Andrew Ashton and David De Lorean.
