The 20-year-old, from Dungannon in Co Tyrone, protested her innocence after police officers discovered more than 24lb of cocaine - thought to be worth around £1.5m.
It was found hidden in the luggage of Ms McCollum Connolly and her friend, 19-year-old Melissa Reid from Scotland, who were arrested in Lima a week ago.
The video shows Ms Reid being questioned by detectives.
She tells them: "I was forced to take these bags in my luggage." When asked if she knew they contained drugs, she adds: "I did not know that."
The pair, who had both left home for separate holidays in Ibiza earlier this summer, were arrested by the National Police of Peru last week while trying to board a flight to Madrid.
Sean Walsh - an Irish-American archbishop with the Eastern Catholic Church, who visited the pair in a police holding centre in Lima - claimed the two women were forced to act at gunpoint by Colombian gangsters - and had no choice but to follow orders.
They told me that there were a group of Colombians that actually took them at gunpoint and threatened them.
Archbishop Sean Walsh
The Archbishop added that the women were held for a while by the gang before being taken to Morocco and back again to Peru.
"I don't know how that happened, and I don't know how they got over to Peru," he said.
"There's no direct flight from Morocco, they go through Spain probably, but if they threatened them in some way that to me seems like a credible defence."
Archbishop Walsh, who has been working with prisoners in Peru for several years, said he met with the two women for half an hour in the police offices of the holding centre.
"If they have been coerced or threatened as I think they are going to argue, then the fact that they physically had it in their possession may not mean that they were intentionally or wilfully doing it," he said.
"If they were forced with threats on their life or something then they might not have gone through with this."
The cleric said he believed the women would plead innocent on the basis of coercion.
He also said he did not see the cells the women were staying in but believed they were being treated well, and said one of their chief concerns was for their families.
Peter Madden, of Madden & Finucane, is representing the family of Ms McCollum-Connolly.
He said that the young woman has been questioned by the police, has denied involvement in any criminal offence and will be appearing before an examining judge shortly.
"The family fully support her and they are making arrangements to travel to Peru. They have contacted support groups in Lima to ensure that her current needs are met.
"I am arranging legal representation for her in Lima."
Michaela's family are obviously shocked and distressed by the recent events but are confident that Michaela will be exonerated.
Peter Madden, legal representative
Mr Madden continued: "I spoke to Michaela last night and she emphasised that she denied that she was guilty of any offence. She is well. She is not on hunger strike. She is finding it difficult to cope with the current situation, so far from home, but is optimistic.
"The family want privacy at this time and hopefully this will be respected by the press and media."
Amnesty International says it has concerns about prison conditions in Peru.
Patrick Corrigan, NI Programme Director, said: "The number of foreign nationals held in Peru has been growing steadily in the last few years, due to an increase in arrests for cocaine trafficking out of the country.
"Inmates have very limited access to medical care, with prisoners having to pay for many basic services, including sufficient food and drinking water, according to some reports.
"Based on these reports, Amnesty International would be concerned that prison conditions in Peru do not meet international standards."