We just took over property on 4/1. Prior lease has lead paint clause that states
"lessor has no knowledge of lead based paint or lead based paint hazards in housing."
"lessor has no reports or records pertaining to lead based paint and/or lead based paint hazards in the housing"
Many states require that a rental property built before 1978 (or is it 1976?...right around there) be professionally tested for lead and then remediated if need-be. The state then issues your property a lead certificate. For example, in Maryland, we have Lead-Free, Limited Lead-Free, and Lead Safe certificates.
I'm not sure what you're specific question is, but you should quickly find out your state and county's rental requirements.
What state is the property in?
I'm in Massachusetts which has some pretty strict lead laws and is generally viewed as tenant friendly. I've found the State generated info online geared towards renters is a great resource for landlords. Spells out a lot of things to look for and has a lot on lead paint. You'll also see a lot of lawyer pages that have good information geared towards tenants which is helpful to landlords.
See if those resources can help you find out if the have the option to request a lead test.
We're in Kansas. Checking
Check your local state/municipal websites as they are a wealth of info. Massachusetts for instance maintains a website that indicates which homes have had testing for lead paint. I'd say 50% of the homes listed as 'unknown lead' in our MLS are actually lead positive. It opens the agents and owners up for litigation in the long run.