This led to a days-long manhunt that stretched from the western part of the state near Buffalo all the way to South Carolina.
During his time fleeing authorities, he embarked on a further crime spree including alleged arson and the kidnapping of an elderly couple at gunpoint at their home in Pennsylvania.
Taking their car he drove them to South Carolina before releasing them unharmed, Fox News reports.
They were reported missing on 20 May by Pennsylvania police and were found by South Carolina Highway Patrol on 21 May in North Charleston.
Mr Burham was eventually arrested on 22 May. Authorities found a note to his father in the car he had stolen.
According to court filings, the note in part says: “I’m not sorry for what I did, however, I do feel terrible about the children.”
He also claimed to have quit drinking the day before he shot Ms Hodgkin and apologised for all the problems he had caused his family.
Before the murder of Ms Hodgkin, Mr Burham was already wanted on charges of sexual assault against her.
He was also allegedly seen on the day of the murder on his ex-girlfriend’s Ring doorbell camera as he tried to break into her house before setting fire to her car.
Mr Burham was being held while awaiting extradition to New York to face the murder charge when he escaped from the Warren County Pennsylvania Jail.