Phone screening includes number of people, pets, income, when can they take possession, smokers, and criminal history.

We do however look carefully at the credit history.

If they do not score enough points (or just blatantly miss a stated criteria, like no prior evictions) in that initial subtotal I do not move forward.Use objective criteria, like how long they have held their job, % of rent to income, how long they have lived at past addresses, how long they intend to stay, stated criminal history, whether they provided bank accounts, etc to put a score to your hunches.You can also drag your feet on denying, I normally wait until I have an applicant who has accepted to deny the rest of the applicants. 

I have a portfolio of cash flowing rentals in eastern Kern County (about 40 minutes from Bakersfield) and the monthly networking meetings we have in Bakersfield are attended by many cash flow oriented local investors.  

They do see it though when they pull up the claim history report but i think 1 claim does not do much.

What documents do they require, what credit scores do they allow, how do they verify previous rental history, etc.?

I think previous rental history is the most crucial thing as a predictor of their future.The more people you have unrelated, the more chance for one or 2 of them to want to leave at some point along the way when a girlfriend or other situation arises.

Looking at a listing and in the Property History section it lists the "Foreclosed Date" and the price. 

If there's a tight deadline, go down to city hall on Hamilton St and ask the Bureau of Standards and Safety to provide any permit history.

I'll need to check my credit score to see whether any of my Canadian history is accessed by the U.S. credit bureaus.