Her death gave rise to widespread public grief, as well as outrage over violence against women, and tens of thousands of people attended vigils in her memory.

The President of Ireland, Michael D. Higgins, the Taoiseach, Micheál Martin, and other Irish government ministers attended her funeral in Mountbolus, County Offaly, on 18 January.

In the days following Murphy's death, the Garda Síochána (Irish police) questioned 31-year-old Slovak Romani father-of-five Jozef Puška, who was subsequently arrested and charged with her murder.

[6] In March 2021, she began working as a substitute teacher at Scoil Naomh Colmcille, a primary school in Durrow, County Offaly, around 8 km (5.0 mi) northwest of Tullamore.

She was last captured on CCTV at 2:55 p.m.[22]Geolocation data from Murphy's devices showed that she crossed Digby Bridge at 3:16 p.m. and headed westward back towards the Daingean Road car park.

[19] One of the cyclists noticed the mountain bike in the hedge and discovered Murphy's motionless body on her back in the adjacent ditch, her face covered with matted hair and blood.

[42] Numerous other vigils took place throughout the country, in locations including Dublin, Galway, Belfast, Limerick, Cork, Waterford, Kilkenny, Navan, Maynooth, Drogheda, Sligo, Ballina, Derry, Omagh, and Armagh.

[43][44] Murphy's family attended a candlelit vigil near the murder scene, where her father and his Best Foot Forward bandmates played her favourite song, "When You Were Sweet Sixteen.

"[49] The Taoiseach, Micheál Martin, said "the entire country is devastated and shocked by the violent and barbaric killing" and said the murder had "united the nation in solidarity and revulsion.

[64] The Kilcormac–Killoughey GAA senior camogie team also formed a guard of honour, while musicians who were friends or colleagues of Murphy played traditional Irish music at the Mass and at her graveside.

Her godparents brought to the altar items to symbolise her life, including a musical instrument, a camogie stick and Kilcormac–Killoughey GAA jersey, a family photo, and a schoolbook.

[66][68] Describing Murphy as "a woman who lived the short years given to her to the full", Bishop Tom Deenihan of Meath called her death "a depraved act of violence" but said it had "united the country in grief and support.”[66] In his homily, local parish priest Fr.

[78] The initial suspect was a 40-year-old man,[79][80] whom Gardaí detained two hours after the murder based partly on descriptions given by an eyewitness,[39][81] but whom they released the next day after eliminating him from their investigation.

On the late morning of 13 January, Gardaí and paramedics had been called to an apartment in Crumlin, Dublin, where a Slovakian national told them that he had been stabbed the previous day in Blanchardstown.

[36][85] Gardaí who were investigating a double stabbing incident in Blanchardstown interviewed the man at the hospital that afternoon, initially regarding him as a potential third victim in that attack.

[15] Upon returning to Blanchardstown Garda Station, the Gardaí reported the interview to Detective Inspector Shane McCartan, who concluded that "There were a lot of pieces of a jigsaw puzzle that just couldn’t be put together, that just did not add up.

[91] A Dublin Garda sergeant obtained a search warrant and joined the two detectives as they interviewed the man in a private room at St. James's Hospital on the evening of 14 January, with a Slovakian interpreter translating via speakerphone.

[100][101][48] At 7:42 p.m. on 19 January, Gardaí charged the man with Murphy's murder and identified him publicly as 31-year-old Jozef Puška with an address in Mucklagh, a village around 5 km (3.1 mi) southwest of Tullamore.

[107] A Slovak Romani, he grew up in Lučivná, a ski resort village in the Poprad District of northern Slovakia, in the foothills of the High Tatra Mountains.

However, Mr. Justice Tony Hunt decided that the evidence was admissible in court, stating that the CCTV footage did not breach Puška's privacy rights, and that Gardaí did not require a medical assessment before interviewing a criminal suspect.

[85] Another witness, a local woman, testified that she had been out walking her dog on the canal towpath after 3:00 p.m. when she saw a man matching Puška's description cycling a mountain bike with bright green forks.

[122][123] Puška had previously admitted to Gardaí that, upon returning home, he had changed clothing and asked another member of the household to burn the garments he had been wearing during the day.

She stated that the chance of the male DNA found under Murphy's fingernails coming from someone unrelated to Puška was one in 14,000, based on a database of European ethnic groups.

[131][100][129] Speaking through a Slovakian interpreter, Puška claimed in his defence that he had been cycling on the canal towpath when a man wearing dark clothing and a surgical mask shouted at him, pushed him off his bike, and stabbed him three times in the abdomen.

[132][133][134] The defence contested the validity of Puška's confession at St. James's Hospital on 14 January, noting that he was recovering from surgery at the time and had received a dose of oxycodone for pain relief 2 hours and 20 minutes before his interview with Gardaí.

An expert witness for the defence, a doctor described as an accident and emergency and intensive care specialist, stated that Puška could have been experiencing side-effects of that drug, including confusion, hallucinations, and irrational thinking.

Citing a study showing no effects on the mood or behaviour of people who had taken less than 10 mg of oxycodone, he stated that there was “no evidence to suggest [Puška's] admission was related to any drug”.

[16] Persistent rumours that she had known his children through her job as a teacher, and that he had killed her in an act of revenge after she reported child welfare concerns to Tusla, were debunked during the trial.

He added: "We have to, once and for all, start putting the safety of not only Irish people but everybody in this country who works hard, pays taxes, raises families and overall contributes to society, first."

On a BBC Northern Ireland current affairs programme The View, journalist Kitty Holland criticised these aspects of Casey’s statement, claiming that they contained "elements that were not good” and were "latched onto" by the far right.