Does the state legislatuers have power to oversee state agencies

In most cases, yes.

In some other cases, no

it all just depends on where it is and whats happening

Legislative Veto of Administrative Rules

Although state legislatures have delegated that authority to executive agencies, they have carefully protected their authority to review and, in most instances, approve administrative rules to ensure that they comply with statutory authority and legislative intent.

Explanation:

can not you sorry