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Stop and inspect vehicles for safety violations
LAPD officers are usually deputized in the county so if needed they can respond to situations when county officers are busy, but LAPD does not have authority over LA County Sheriffs Dept.
Officers of the New Mexico State Parks, state police, and county sheriffs have the authority to stop and inspect vessels for safety violations.
Stop and inspect vessels for safety violations
County Sheriffs do not have the authority to call out the Guard. That's done by the governor of the state or the president of the US.
The principal governing authority of Georgia counties is a county commission. They are elected by the registered voters of the county.
As of 2021, there have been a total of eight sheriffs in Clayton County, Georgia.
They have no authority to do so.
You can find a list of Florida sheriffs at the URL associated with this answer.
An officer's "commission" is the authority granted to them by the jurisdiction in which they are authorized to act as a law enforcement officer (e.g.: town, city, county, state, federal). All officers carry agency issued identification cards which both identifies them and gives them the authority to act.
There is only one Sheriff per county.
You have highway patrol or state troopers, you have county sheriffs departments and city police departments. The above relates to the USA, in other countries police and their ranks and specialisms are organised differently.