Foreign citizens are obliged to register their stay In Poland. Otherwise residence is illegal and it could be a reason of expulsion from Poland without the right of entry for a few years.
Citizens of member states of the European Union enter the Republic of Poland without a visa. They do not need to register their short-term stay, i.e. shorter than three months. Citizens of member states of the EU who reside in Poland for more than three months are obliged to register their stay with the authorities.
EU national should provide:
Citizens of countries other than a member state of the European Union enter the Polish territory on the basis of an obtained visa. If they want to extend their stay they need to apply for residence card at least 1 day before the visa expires.
Non-EU citizens should provide:
Residence permits for a specified period of time are issued to foreigners on the basis of an administrative decision of the provincial governor of Kujawsko-Pomorskie made on the basis of an application. More information: http://www.bydgoszcz.uw.gov.pl/en/aktualnosci/for-foreigners.html