The first occurred at around 4.15pm on Thursday 16 January 2014, when a vehicle hit a car parked on Beckfield Lane.
Due to debris left at the scene it is believed that the vehicle which caused the damage is a blue Ford Focus.
The second incident occurred at 3.20pm on Friday 17 January 2014, at the junction of Mount Vale and Knavesmire Road.
It involved a pedal cycle, which swerved to avoid a VW Golf which pulled out in front of it, and another vehicle. As a result of the collision the rider of the bike suffered minor injuries and the cycle was badly damaged.
PC Nicola Elliot, of York Safer Neighbourhood Team, said: If you witnessed either incident or can help to identify the driver of either the Ford Focus or VW Golf, I urge you to contact the police straight away.
I am particularly keen to speak to anyone who works for a vehicle repair shop who was asked to repair the body work of a Ford Focus and urge them to get in touch.
Anyone who can assist with rather of these enquiries should contact York police on 101, select option 2 and ask for Nicola Elliot. Alternatively, information can be emailed to firstname.lastname@example.org