Inherited Tenants; no access to app/screening info

[Susan H.]

I purchased a tenant-occupied SFH in December. The previous owner did provide a copy of their lease (3 generic pages) but no info/record of application or background/credit check screening report. Comments by prior owner have me doubting any screening was done. She confirmed tenants have paid on time. Both tenants and previous owner signed an Estoppel form prior to closing, so I knew the rent (below market) and lease termination date (7/31/18).

I intend to send them 90-day notice of intent to raise the rent by 2% which will bring the unit a bit closer to market rates, and to advise them that any renewal is dependent on them signing my own (much more detailed) lease.

My question: is it reasonable to require they complete an application and screening and meet my qualifying criteria prior to offering the new lease? There's no fee for my application, but there is a $30/per adult fee for the background/credit check.  I have no knowledge of their income, background, etc. and that makes me hesitate about offering a lease renewal.