The federal and state governments are divided into three branches:

Agencies that do enforcement or rulemaking must be in the executive branch.  Public health agencies are classic executive branch agencies at both the state and federal levels. Independent agencies are agencies that are technically in the executive branch but which are run by directors or boards that are not directly answerable to the executive.  At the federal level, the SEC is an independent agency.  At the state level, some states and local governments have boards of health that try to protect the health department from political influence.

Most states do not have a single executive branch.  Instead they have several, each headed by an independently elected official.  For example, most states elect an attorney general who runs the state legal office and a governor who runs other agencies.  The governor cannot tell the attorney general what to do, which can be very problematic if the governor must depend on the attorney general for legal services.  Many states also elect state auditors, insurance commissioners, and other state wide offices.  In states where only the Attorney General can provide legal services, the health department, which is under the governor or a board of health, cannot make its own legal decisions or appear in court unless the attorney general's office approves and provides counsel.