The Governor of that state
The Governor of each state is the head of that state's executive branch.
Assuming you mean, "Which branch of the Federal government has two members from each state? The answer is 'The Senate'.
what are the responsibilities of the legislative branch
State supreme courts (or their equivalent) are part of each State's Judicial branch.
The President makes the state of the union.
There are two Senators from each American state.
"Separation of powers," Means that each branch of government is independent
Federalism divides power between the state and national governments. The separation of powers ensures that in both state and national government each branch of government is responsible for certain things and each branch of government balances each other.
In the US federal government, the legislative branch has two chambers, the House of Representatives and the Senate.
The Articles of the U.S. Constitution describe each branch of government.
In the United States the legislative branch of the US Senate, is composed of senators. Each State has two senators in the Senate.
Executive branch, Legislative branch, and judicial branch. No, there are two houses that make congress. The Senate with 100 members that have 2 from each state. The House of Representatives with 435 members.