Grand Theft Auto: San Andreas

A motor officer on a HPV-1000, GTA San Andreas.
Appearance
Motor officers in the game make up the San Andreas Police Department and ride HPV-1000 motorcycles, which, like other motorbikes, are far more manoeuvrable, agile and compact than cars. The use of motorcycles also allows police officers to fire their weapons at criminals from any direction while in a chase. While mounted, motor officers will fire upon the player even if they have only acquired a one star wanted level.
Motor officers are equipped with uniforms consisting of a black with white turtle shell helmet, a black leather jacket, biker boots, sunglasses, fingerless gloves, and black striped pants, They are armed with nightstick and pistol, and are depicted as African American men (with African American accents). Their attire, as well as their choice of motorcycle, mirrors that of Los Angeles motor officer units employed during the early 1990s, as well as the depiction of both a T-1000 assuming the guise of an LAPD motorcycle officer in the 1991 film Terminator 2: Judgment Day and one of the "Death Squad" SFPD motorcycle officers from the 1973 film Magnum Force.
Like SWAT teams, motor officers in GTA San Andreas are one of the only police units found around the state of San Andreas that are consistent in all areas. (e.g. the character model remains the same in all areas despite the fact that San Andreas State Patrol are found in respective areas and each city has a different police force). For this reason, they sport San Andreas Police Department markings instead of a specific police department designation. Motor officers are most likely the state police, as they appear in each city.
Behavior
Motor officers behave like all other police officers. They will pursue fleeing criminals, make arrests, and use a night stick and/or pistol when facing resistance. Their only extra behavioural phenomena is that they will shoot at the player from their bikes regardless of his or her wanted level (this happens when the player has a wanted level and then saves the game, the Motor Officer will still shoot the player). Motor officers usually give chase on wanted levels from one to two stars. They will often drop pursuit of the player after he or she has acquired three-star wanted level, being replaced by larger, more well-equipped units. During the mission Reuniting the Families, motor officers used risky methods of attempting to stop the car even though there were armed passengers by jumping onto the hood and trunk of the car trying to pacify the passengers.
Grand Theft Auto: Vice City Stories

A motor officer on a VCPD WinterGreen, GTA Vice City Stories.
Appearance
Motor officers in GTA Vice City Stories are similar to those in GTA San Andreas in several regards. They possess similar equipment, including a beige turtle shell helmet, sunglasses, and boots (but otherwise feature the same beige-and-brown Vice City Police Department uniforms worn by other officers), as well as standard issue nightsticks and pistols. However, these officers ride VCPD WinterGreens, a police variant of the WinterGreen motorcycle.
Behavior
Much like the motor officers in GTA San Andreas, in GTA Vice City Stories they will only give chase at a one to two star wanted level. After acquiring a higher wanted level, Police Cars arrive to take over pursuit.
Grand Theft Auto V

A Motor Officer on his Police Bike in GTA V.
Appearance
Motor officers in GTA V are officers of the San Andreas Highway Patrol and wear uniforms resembling the California Highway Patrol's. They wear beige pants and shirt, with a blue tie and black boots. Officers wear blue helmets and sunglasses, and have a two-way radio clipped to their shirt, along with a standard belt. Motor officers carry Pistols.
Behavior
Officers act identical to all GTA V police; by approaching them they will make warnings to maintain distance, and afterwards could give a one-star wanted level. Officers monitor speeds on the side of the road, and they rarely join police chases. They will only join if the suspect is near them.