It happened in Salisbury Street around 5:00pm on Monday (June 13) and a pedestrian was left with serious injuries.
Police said a large black car did not stop at the scene, and they launched an appeal for witnesses to come forward.
The pedestrian remains in Victoria Hospital, Kirkcaldy.
Last night officers said the car has been traced and a 38-year-old man is subject of a report to the Procurator Fiscal in connection with road traffic offences.
Road Policing Officers are continuing to appeal to any witnesses to the crash, or anyone in the area at the time who has information or private footage to contact them through 101 quoting reference 2672 of 13 June.