How long do the police have to charge you with a DWI?
It is not the police that charges one with the crime of driving under the influence of alcohol or a controlled substance. It is the district attorney's office in the county and state where one has been stopped and arrested for that offense (or cited).
Typically due to the backlog of incidents around the holidays and Christmas furloughs, the district attorney's offices in most states in this country are behind in issuing complaints. From my experience I estimate that assuming you were stopped for the offense that you are writing about, a criminal complaint (assuming one is warranted) will be filed within 60 days of your stop.