In 2012, Mulligan was sentenced to three months' home detention for assaulting his sister.
But Southern Police Senior Sergeant Craig Brown said Mulligan was not a danger to the public.
Officers were still making enquiries in Invercargill in an attempt to locate Mulligan, he said.
"He's not specifically [dangerous]. The charges that he's on aren't charges that would prompt that," Mr Brown said.
"Getting him back in the bounds of the bracelet [is the aim]."
Mulligan is believed to be the 19th prisoner who is currently on the run from the electronic monitoring device.
Prime Minister John Key said on Thursday he was "a little bit surprised" to learn 18 prisoners had slipped their bracelets, but that the number was only a "tiny fraction" of the almost 3500 electronically-monitored prisoners in the community.
"I don't know all the details about how they're actually getting them off but as a percentage of the people that actually wear an electronic bracelet it's a very tiny fraction of those.
"Obviously one is one too many."
There are 3232 offenders on the electronic monitoring system introduced in February - 1832 are also monitored via a real-time GPS system.
Convicted child-sex offender David Livingstone was caught this month after he cut off his bracelet.
Last year, Tony Robertson murdered and raped North Shore woman Blessie Gotingco while on monitored release for child-sex offending.Corrections assistant northern commissioner Alastair Riach said alarms were raised immediately if bracelets were cut.
"We know who they are. Police will be prioritising, depending on the risk, the effort they will put into locating these people."
Invercargill police are urging anyone with information to contact them on their Facebook or by calling (03) 211 0400.
Information can also be left anonymously through Crimestoppers on 0800 555 111.
