In the United States the police department is usually under the local government. In some places the county takes care of all police department activities. In other places the police department is under the state. In some places a combination applies. For example: Texas has policemen hired by local units of government but a Texas Ranger who works for the State can arrest anyone just like a local cop can.
police
He is the Chief Administrator of his agency which is part of the Executive Branch of government.
personnel
The color is a local decision. Generally, in the western part of the US, city police wear blue, county sheriff departments wear brown, and state wear blue or brown.
In the US it can be private, local, county, state, or federal
Local governments spend the majority of their budget on city services such as police and fire departments. Another huge part of their budget is used to maintain water treatment plants and city streets.
The director department place
It's not. Law enforcement is a function of the Executive Branch of government, not the Legislative Branch. The US Attorney General is the chief law enforcement officer of the United States. He is also the head of the US Department of Justice. State and local police departments are likewise considered part of the Executive Branch of government.
All of these departments belong to the executive branch.
What is under the cabinet members that are part of the executive branch of your government?
It is those that take part in it that are responsible for it, not any level of government. If there is legislation against it in your country then it could be local or national. You would need to check the specifics where you live.
A "reserve" officer, is usually either a volunteer, or a part-time officer who has been trained in all aspects of police work and choose to assist their local departments to assist them by increasing their manpower during times of need.