We Czech your papers.

EU citizen registration

If you are an EU citizen, you are supposed to register your stay with the foreign police

You should register your stay within 30 days of arriving in the country. You can register with the foreign police or you can apply for temporary residency for stays longer than 90 days.

The EU prohibits any member country from "requiring" a residency permit for EU citizens. Although be required to register your address with the authorities.
The Czech foriegn police have sommething called registration and rather than a residence permit. and say that you have the "right" to it apply for one.

Reistration is of no practical use and is a minimum requirement.
If you pan on living in the Czech republic for any length of time (more than 90 days) then you should consider a (temporary) residence permit.
The foreign police are currently issuing a "temporary" residence permit for EU citizens. Although "temporary" by name, the permit is without an end date.
If you wanta contract for a mobile phone, buy a car or apply for a credit card, you will need some type of residency.