"We are appealing for witnesses who saw Ms Morris fall from the car to come forward, particularly anyone who saw the vehicle she was in."
She fell from a silver Ford Mondeo.
"We'd like to thank passers-by who stopped and assisted Ms Morris. Now we need your help to explain the circumstances surrounding her death."
Morris' family have been spoken to and are being offered ongoing support.
Police are investigating on behalf of the coroner.
A memorial for Morris, who friends called "Morrie" is scheduled for Sunday.
Loved ones will gather with balloons at midday near the New Brighton pier.
Friends came together on Facebook to share tributes to Morris.
"You sure have left a big impression on a LOT of people," one friend said.
"You always were a choice lil lady ... you had the kindest biggest heart ... I'll never forget the best years of my life was spent kickin it with you ... such a heartbreaking thought knowing you're not here anymore."
Another person told Morris to "fly high beautiful", and another said she was a "beautiful soul".
Cottam asked that anyone who saw Morris fall from the car or has any further information to contact Christchurch police on (03) 363 7400.
Information may also be provided anonymously to Crimestoppers on 0800 555 111.