The incident happened at around 6.15pm on Friday 24 November 2017 in Acland Road car park.
The victim – a local woman aged in her 70s – walked along the footpath between South Walks House and the rear of Goulds department store, when she became aware of someone behind her.
She continued walking across the car park when she felt someone grab the handbag she was carrying, causing her to lose her balance and fall to the ground.
The victim kept hold of her handbag, but the offender then dragged her a short distance along the ground. He then verbally threatened her before he managed to pull the handbag away and run off in the direction of Acland Road.
She was treated by paramedics to an injury to her head after falling to the ground, but did not require hospital treatment.
The offender is described by the victim as a man who was very thin and grubby in appearance and was wearing a dark-coloured hooded top with the hood up.
Detective Constable Emma Swann, said: “This was a terrifying ordeal for the victim to endure. The incident happened at a busy time of the day and I am appealing to anyone who saw someone acting suspiciously in the area or witnessed the robbery take place to please contact Dorset Police.
“In particular, the victim states she saw a car parked in the car park with its lights on and thinks there may have been someone within the vehicle that could have witnessed the incident.
“We managed to locate the handbag nearby thanks to assistance from the dog unit, however a quantity of cash had been stolen.
“We have been making house to house enquiries and are currently reviewing CCTV footage to see whether the offender described was caught on camera in the town and investigations are ongoing.”
Anyone with information is asked to contact Dorset Police at www.dorset.police.uk, via email firstname.lastname@example.org or by calling 101, quoting occurrence number 55170183432. Alternatively, contact Crimestoppers anonymously on 0800 555 111 or via www.crimestoppers-uk.org.