It comes after a 16-year-old boy was arrested over racist and sectarian comments she made on Twitter over the Glasgow Clutha bar tragedy.
As yet it is unclear whether mum-of-two Bingham — the daughter of murdered north Belfast UVF boss John Bingham — is being investigated by police.
But a PSNI spokesperson told Sunday Life “appropriate action” would be taken where a criminal offence has occurred.
The post — which has now been removed by the 40-year-old — read: “were any taigs hurt in that helicopter crash?”
She added: “PMSL (p***ing myself laughing) fs only askin.”
Her comments were made as rescuers trawled through the rubble of the Clutha bar where the police helicopter crashed on November 29.
Three crew members and six revellers were killed when the Police Scotland aircraft crashed. A 10th victim died in hospital on Thursday.
Last week Scotland’s most senior lawyer, Lord Advocate Frank Mullholland, called for a “robust prosecution policy” over any hateful comments
made online about the crash. He said: “Prosecutors must take a hard line against this kind of hate crime.”
Asked whether police were investigating any comments made on social media in regards to the crash, a PSNI spokesperson told Sunday Life: “When a report is made to police regarding information posted on social media sites, officers will investigate and where a criminal offence has occurred, appropriate action will be taken.”
In a brazen interview with Sunday Life last week north Belfast woman Liz — who claimed her comments had not broken the law — attempted to justify the hate-filled message.
“The way I am looking at it now, yes it was a bad judgement,” she said.
“But I haven’t broken any law because I didn’t say I wish this, that or the other. I wasn’t spilling hate.”
She then added: “Whether you like it or not taig is a term we use whether you find it offensive or not.
“We refuse to use Fenian because they are not Irish warriors or even warriors in our eyes.”
She added: “I have a good relationship with many Catholics from Ardoyne, and from other communities.
Bingham claimed she was driven to making the “nasty” and “provocative” comments after being bombarded with death threats. “I have Post Traumatic Stress Disorder and I am constantly bombarded with hate mails,” she said.
“My 12-year-old disabled daughter has also received them. I just had enough.”
Liz, who lives close to the Shankill, says she has been the target of online abuse since becoming one of the key figures at the Union flag protests.
She claims posts and pictures from her ‘set to private’ social networking accounts have been leaked to the pages of the satirical group LAD (Loyalists Against Democracy).
“So I decided to go down the route of posting something controversial, something nasty — see if it turns up on the LAD,” she said.
“I just wanted to find out who it is that is hiding in there.”
Bingham, who left her home after it was recently attacked, added: “The way I am looking at it now, yes it was a bad judgement, but I done it.”