Because most U.S. police agencies have been created and funded by the local communities, and because they were created at different times, there are many variations in how the agencies are organized and financed. In general, city police are funded by the municipality and headed by a police chief, either appointed by the mayor or elected. Counties employ patrolmen and sheriffs, who usually answer to an elected county official.

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http://www.answers.com/topic/police

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Note added at 28 mins (2011-08-09 00:37:53 GMT)
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http://sheriff.lacounty.gov/wps/portal/lasd

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Note added at 30 mins (2011-08-09 00:40:38 GMT)
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Please check out the above link of Los Angeles County Sheriff's Department

The whole county is under the jurisdiction of the sheriff which is higher than the city police and lower than the state police. Some rural areas in the US have no police departments so they fall under the jurisdiction of the sheriff and if there is no sheriff department they are directly under State Police.
110% sure

Police Departmdent = دائرة شرطة
The Sheriff in America is an elected person. He does not report to anyone except to the people who elected him. On the other hand, the Chief of Police is an appointed person who reports to the Mayor.