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:

there are many ways of getting involved on your local party. attached you will find the brochure that describes some ideas: go ahead and visit your local hq, become a volunteer on your comnunity or struggle up for your own ideas so you can make them real.

“i think it is very plausible that if there are five votes to end the death penalty, it could be with the people who are on the court right now,” - smith

so basically it is not clearly and consistently imposed