During the incident two people were reported to have driven a car towards two pedestrians in Institute Road.
One of the pedestrians was seriously injured following the collision which happened at around 11.15pm on Thursday 4 November
Following the incident officers arrested a man in his 20s from Sheerness, and a second man in his 40s from Chatham.
Following enquiries and a review of CCTV, officers are seeking witnesses who may be able to identify other people who may have been in the car at the time.
The suspects and victims are believed to be known to each other.
Anybody with information is urged to call Kent Police on 01795 419119, quoting reference number 46/224473/21.
You can also contact Crimestoppers anonymously on 0800 555111, or by using the online form on their website by following this link: https://www.kent.police.uk/news/news-search/