Old Westgate and number of roads nearby have been closed off today while investigations continued.
Three people who were inside the car when it crashed have not been held by police, but two arrests have been made.
A West Yorkshire Police spokesman said a car drove into a barrier outside Dewsbury Police Station at about 10.47pm yesterday.
He said: "Three persons in the vehicle were uninjured and enquiries are ongoing this morning to determine the full circumstances.
"The incident is not terror related and two other men aged 17 and 29 have now been arrested in connection with what took place.