Final answer:
A state legislature is responsible for deciding on funding for police and fire departments, as it is involved with lawmaking that includes resource allocation for public services in the state. Option c is the answer.
Step-by-step explanation:
The matter that a state legislature would be responsible for deciding is funding for police and fire departments. State legislatures are primarily involved in lawmaking at the state level, which includes allocating state funds and resources for public safety and services, among other responsibilities. This includes decisions around funding for local police, fire departments, and other critical emergency services provided within the state. These legislative bodies also focus on constituency service and oversight of public policy implementation. They do not, however, rule on errors made by lower courts, manage local mayoral elections, or conduct impeachment trials for governors, which are responsibilities of the judiciary or local governments.