What branch of the government does a police department fall under?

A police department is part of Justice. It enforces the laws.

Actually, a police department is typically a part of the executive branch of government. The executive branch is responsible for implementing and enforcing laws. Police departments are usually overseen by either a mayor, a city manager, or a police commissioner who is accountable to the executive branch. However, it's important to note that the specific structure can vary depending on the jurisdiction and level of government. In some cases, there may be state police departments that fall under the executive branch of the state government, or federal agencies such as the Federal Bureau of Investigation (FBI) that operate under the executive branch of the federal government.