The man arrested and Ms Morris were known to each other.
"There is an association between Tracey and the man who was arrested," Ms Le Bas said.
Police continue to search for facts explaining Ms Morris' final three days, said Ms Le Bas.
A post mortem examination, carried out yesterday, found the injuries were consistent with a "violent incident", she said.
Ms Morris was last sighted at Phoenix bar on Tuesday 3 January, where she worked as a barmaid and often also frequented the bar as a patron.
A police team has been interviewing her family, friends and associates to confirm her movements prior to her death.
Forensic experts were also working on the crime scene today, she said.
Notices had been pinned up at the bar where Ms Morris worked, asking for the public to come forward with any information they might have on what happened after she left the pub on Tuesday afternoon.
-APNZ