Lead paint issue in multifamily house

[Kenny M.]

Have a bit of a problem here.  I just purchased a multi-family building a few months ago.  There was a previous tenant with a child who's 8 I believe.  They've been in the building for less then a year, and I've owned the building for the last four months.  The child has higher than normal lead levels.  The dept. of health has sent us a notice to remediate the lead paint issue within the next two months.  I already have requested quotes and will be having this taken care of and remedied within two weeks.  When I purchased the home, the previous owner signed off with no knowledge of lead paint being detected.  The renter was given the EPA lead docs and signed off on the notice that since the building was built prior to 1978, there may be lead paint in the building.  

I am concerned with the legal liability from owning the house for just a few months. I am concerned that the tenant may sew.  The house is only worth 52k, so I have no mortgage.  Now, I have no knowledge that they will.  How much liability could I have for four months of ownership?  Plus, I have a signed document from the previous owner that there is no knowledge of lead paint, as well as the tenant signing off on the lead paint notice disclosure.  We just received the notice from the city, and we're already on top of it.  Not sure what else I could had done to protect myself legally.  

Just concerned here.