Murphy was jogging along the Grand Canal in Tullamore, Ireland, shortly after she finished work at 3 pm. She was attacked at around 4 pm on Fiona's Way, a canal walkway just outside the town in Cappincur. Murphy sustained serious injuries consistent with a violent assault and was confirmed to have died from strangulation.
Two women, who were jogging on the opposite bank, saw Murphy being assaulted and ran to the nearest house to phone the Gardaí. Gardaí believe that when the attacker confronted Murphy, she fought back in a desperate attempt to save her life by using her keys.
A Falcon Storm mountain bike was recovered from the crime scene and linked to Murphy's killing. There were reports that another woman was followed by a man on a bike in Tullamore two hours before Murphy was killed. CCTV footage of the bike on the day of the attack were recovered.
DNA evidence of the alleged perpetrator was recovered from Murphy's body, with Gardaí saying "she fought for her life". On 17 January, Gardaí said "significant progress" was being made, as they issued a renewed appeal for information and asked people to come forward if they noticed a man dressed in a black tracksuit and black runners.
On 14 January, Gardaí identified another person of interest. The suspect had presented himself to St. James's Hospital in Dublin with unexplained injuries, which prompted healthcare workers to contact Gardaí. Gardaí carried out a background check, which led to searches of properties in County Offaly and one in Dublin. Two cars were also seized. One was a taxi, which was believed to have transported the suspect to hospital. Gardaí also carried out searches of the Grand Canal where Murphy was killed.
On 18 January, the day of Murphy's funeral, the suspect was discharged from hospital and arrested on suspicion of her murder. The next day, the suspect was charged with murder and identified as 31-year-old Jozef Puška, a Slovak national. That evening, he was brought before a special sitting of Tullamore District Court. He was heckled by a large crowd who had gathered outside the courthouse, and several of Murphy's family stood in court with framed pictures of her. Puška was remanded in custody at Cloverhill Prison to appear again at Clover Hill District Court on 26 January.
Judge Cronin further remanded Mr Puska in custody to appear before Cloverhill court via videolink on February 23.