Emma Ripley, 25, said she was driving down Tempest Road when a car pulled out of the side junction of Trentham Street.
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Footage shows the moment when she got out of her car following the initial crash.
Just moments later, horrifying footage shows the driver speed up to get away from the scene - striking Emma's car in the process.
Emma was just inches away from being struck in the terrifying incident.
Emma, speaking to the Yorkshire Evening Post, said: "I thought he was trying to run me over.
"He rammed the side of the car fleeing."
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A spokesman for West Yorkshire Police said: "At 8.57pm last night, police received a report of a fail to stop road traffic collision in Tempest Road, Beeston.
"A car, believed to be a black Vauxhall Astra, had left the scene after twice colliding with a Renault Captur, causing damage."
> Tony Dorigo recalls Gary Speed memories as giant mural of former Leeds United team mate is unveiledEmma, from Middleton, said she has been left in "disbelief" at the incident.
She added: "He almost knocked me over with my own car.
"I was grateful my one year old baby wasn't in the car seat as he would have hit her directly on that second hit.
"Thankfully her dad had took her home in a separate car."
Anyone who witnessed the incident or who has any information that could assist in tracing the offending driver is asked to contact officers via 101 quoting log 1658 of April 5 or reference 13210168209 or online via www.westyorkshire.police.uk/101livechat