I am a 20-something English girl who has been living in Poland for the past two years. I have never got round to bothering to get a karta pobytu, but the past few times I've flown into Rzeszow Airport I notice that the immigration staff are beginning to scan passenger passports. What info do they get? Can I be refused entry or arrested for not having legalised my stay? Will they even know I don't have karta pobytu?
You don't need a Karta Pobytu as a British citizen unless you plan on staying longer than five years (I believe).
However, you must have legalised your stay here by obtaining "Registration of residence of an EU citizen in Poland". It takes a couple of hours out of your time at the max. I read somewhere today actually a link to the exact information you need but I cannot seem to find it. Anyway, you fill out a form (must be in Polish) a long with a little description of why you're staying here and/or how you plan to support yourself while here (e.g. a job contract, or if not that, then a scan of your bank balance).
When I did it, I just needed a scan of my European Health Insurance Card (EHIC), my passport and my bank balance to show that I could support myself here, a long with a declaration of my reasons for staying here (e.g. "I intend to find work doing X"). You get your surprise visit from the Police at 8am as they interrogate you like a dirty criminal, and then a few days later you get your registration. After doing that, you can apply for your PESEL and after PESEL you can apply for NIP at your local tax office.
As you've been living in Poland for 2 years, I assume you have already done these things, if not... tut tut
When I had my surprise interview by the Police, they asked how long I'd been here. (I believe it was 3 1/2 months?) to which they raised their eyebrow and said "Polish law states that you have to leave after 3 months"... Gulp... "But nevermind".