Polish tenants - what checks should I do?

I have found some suitable tenants to rent my flat, but I am wondering if I should do credit checks?

They are a family of a husband, wife and daughter. The husband is working and has provided me with an employers reference, the wife isn't working as her English isn't very good and their daughter is at a local school. They are also going to provide me with a reference from their current Landlord (they have been at their current place for 2 years and prior to that they were staying with friends)

They have been in the Country for 4 years, would this amount of time be enough to build up a credit history? I am planning to call his employer to verify the reference and to check his salary will cover the rent and I shall call his landlord to check they have paid their rent on time. Would this be enough?

They seem to be a lovely family and I think they will be good tenants, I just haven't had an experience of letting to an EU National before.

Thanks