Ashley Dale, 28, was shot in the back garden of a house in the Old Swan district early on Sunday morning.
It is believed that Ms Dale, who worked in the environmental health team at Knowsley Council, was not the intended victim.
Her family condemned the killing as a “senseless crime” as police made house-to-house inquiries in the local area.
Merseyside Police released footage of a car seen being driven into Leinster Road at around 12.30am – roughly 10 minutes before the shooting was reported.
Officers wish to speak to the car’s driver, or any passengers, as police believe they may have vital information which could help the investigation.
Detective Chief Inspector Cath Cummings said: “Our officers are working round-the-clock to investigate this appalling incident which led to the tragic death of a young woman.
“Our enquiries so far show that a car was driven into Leinster Road, not too long before the incident was reported to police. If it was you driving the car, you were a passenger or the CCTV jogs your memory about anything you might have seen in the early hours of Sunday morning then please get in touch. Information you have could be crucial to our ongoing investigation.
“From reviewing CCTV footage in the area, we have also identified that there were a number of people on foot around the time of the incident. A boxing match had not long finished and so the area was relatively busy with people on foot, going home or into town after the match.
“If you were walking in the area of Leinster Road or on Prescot Road, including the crossroads near the Navigator pub between 12.20am and 12.40am on Sunday morning then please let us know. You may have seen or heard something which could really help us find those responsible.
“Similarly, I would ask taxi and delivery drivers if they were driving in the area between 12.20am and 12.40am and have dashcam footage please contact us.”
In a statement released through the force, Ms Dale’s family said: “Ashley, our girl – our shining light.
“Our hearts are broken into a million pieces.
“Ashley was a hard-working young woman, who had her entire life ahead of her.
“She had just been promoted at her job with Knowsley Council. She had a degree and so many plans for her bright future that had only just begun.
“Her laugh, smile and energy was infectious in any room.
“We can’t come to terms with how this would happen to a defenceless woman in her own home.
“None of this makes sense and our lives will never be the same again.
“A senseless crime that has torn a family apart. Justice needs to be brought.”
Anyone with any information can contact police on 101 or Crimestoppers anonymously on 0800 555 111, quoting reference 22000615873.