Police - City of Round RockRound Rock to participate in Great Texas Warrant Roundup . Our Mission: The Round Rock Police Department, in alliance with our community, provides public.texas rock department,Departments - City of Round RockRound Rock Texas. Skip to . what at the City? The City of Round Rock is divided into a number of departments that are responsible for different aspects of city government. . The Finance Department manages all of the City's financial activity.