The 78-year-old homeless former pianist was killed in a collision with a lorry in Chiswick High Road on February 10.
The story of how she slept in a car outside her former home for many years, refusing all offers of help, made her a local celebrity and hundreds of people are expected to attend her funeral on Saturday (March 7).
Officers at the Serious Collision Investigation Unit have been trying to piece together her last moments and this week said they had gathered all available evidence.
Sergeant Dave Turtle, of Turnham Green Neighbourhood Policing Team, said: "A full and comprehensive review of what happened is now under way, which will also include relevant expertise in regard to collision investigation.
"The enquiry team are keeping an open mind as to the circumstances of the collision and will ensure the local community are consulted and updated in due course once further information is known.
"The Serious Collision Investigation Unit would like to place on record their thanks for all the offers of assistance and send their condolences to the local Chiswick community."
Ms Naysmith's funeral will take place at St Michael and All Angels Church, in Bath Road, Chiswick, on Saturday (March 7) at 11am. She will then be buried at Chiswick New Cemetery.