If the arrest was recent
Start with the county jail
Someone just arrested in the District and not released is held in a DC Department of Corrections facility - the DC Jail (Central Detention Facility) or the Correctional Treatment Facility - because DC is a single city with no counties and no county sheriff jails.
There is no public online DC DOC inmate-search box: to confirm someone is in custody and where, call the DOC Records Office at (202) 523-7060 (open weekdays), or use VINELink (vinelink.com, choose District of Columbia) to check custody status and register for free alerts; DC's VINE line is 1 (877) 329-7894.
People sentenced for DC felonies are moved into the FEDERAL Bureau of Prisons and are found through bop.gov/inmateloc, not a DC tool.
DC has no counties and no county sheriff jails; the DC Department of Corrections runs the only local jail facilities. There is no online DC DOC roster - use the DOC Records Office (202) 523-7060 or VINELink (District of Columbia). Sentenced DC felons are in the federal Bureau of Prisons (bop.gov/inmateloc).