While we're "technically" an arm of state party per FEC law (at least with federal candidate support), we're generally left alone. State Party has some influence, but the main thing they've done in my time as either chair or officer in state/district committee is assist us when we asked. They helped out the 8th on a project we did in 2010. They've publicized our events. If I call them, they're good with responding to me. I can ask for advisement, but they generally don't like to micromanage counties/districts.

Did they tell us how to do things? Only with the Victory Center when they have their own projects. Other than that - as far I know - only when it came to convention procedures or matters which affect state party. We can't exclude elected delegates at convention. Precinct Delegates get priority for state. Names of delegates/alternates must be turned in. Convention date/time is set across the board.  

We're mostly autonomous. The one point of contention there has been in the past is in regards to victory center and campaign strategies.

Is there a role in state leadership regarding districts? That's a good question. If so, how much and in what regard. The 8th and Livingston in that regard has been relatively tame, but I know of at least two absolute horror stories regarding treasurers. What you describe doesn't look good either. Historically, we policed ourselves.