If the house was built before 1978, there may be lead in the paint. The only way to know for certain is to have it tested. Personally, I wouldn't bother. Just sand off the bad paint and repaint with latex to seal, and be sure to clean up the paint debris from the work. BTW did you give your tenant the lead paint disclosure during the lease signing?
Lead was an expensive additive to paint used to extend its life, so you can probably estimate the likelihood that it was used on your house--for instance I have a 1948 condo built by and for returning servicemen at the end of WWII to put the men to work. Everyone swore it had lead because of the age. I put in new windows last year and had to have it tested because of the new law; test came back negative, which makes sense because why would government "make work" construction use high end materials?