The incidents took place in the Tayto car park in Princewood Road.
The black Vauxhall Corsa first had a piece of wood inserted into the air valve of a rear tyre sometime between 11pm on October 16 and 5am on October 17.
Then, between 11pm on October 21 and 5am on October 22, two nails were inserted in each of the offside rear tyre and nearside rear tyre.
Police say they believe the car was deliberately targeted.
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Anyone with information can contact Northamptonshire Police on 101.
Alternatively, they can call the independent charity Crimestoppers anonymously on 0800 555111.