I've already given drug screens to 5 people going there for work. 

I would be sure to screen my tenants as usual, but i would then be able to sleep at night. 

I’ve tried to do some of this myself at the court house but found it hard to use their records and I’m not confident that I was able to cover it well.

This time, I record the dampness over video, and also discover what appears to be black mold that I can see underneath the cracks of the floorboard.

@Anthony Heatley, look up the property records with the town.

Also ensure you screen your tenants well... there are many programs on the market that will help screen, but I find social media is a great place to start.  

You COULD place the property into a Land Trust with the LLC as the beneficiary with your partner and you as the trustees (managers,) which would help conceal your names from public record.

The time and effort involved with screening and background checks seems difficult to handle so far away.   

I would screen everyone including the new tenant don't take the tenant unless YOU think it is a good one.

@Simon W. it appears on the right hand side of the screen usually!