It's possible now to do this online, however (as well as being more expensive) it requires that you have a "verified electronic signature".
I don't know how it is in this case, but for doing most administration staff that is available online, it's possible to use a "trusted profile", which is free, instead of "verified electronic signature". You must register on the website, send (through the website) an application for a "trusted profile" selecting a point to which you will have to physically go to confirm your identity (there are such points in Polish embassies and consulates) and go to this point with your identity card or a passport. Then you will be able to use those services.
To use this online administration platform (it's called ePUAP), you must have a PESEL number. If you don't have it, you can use only an electronic signature.
But it seems, you can also send the application for this certificate by post: bip.ms.gov.pl/pl/rejestry-i-ewidencje/krajowy-rejestr-karny/
You need this application form: bip.ms.gov.pl/Data/Files/_public/bip/krk/formularz_krk_osoba.pdf (PDF), bip.ms.gov.pl/Data/Files/_public/bip/krk/formularz_krk_osoba.rtf (RTF)
Fill it in:
- Nazwa i adres... (upper left corner) - your address (they will send it there)
- Data wystawienia - Current date
- Numer PESEL - your PESEL number, if you have it
- numer paszportu... - your passport number, only if you don't have a PESEL number
- Nazwisko rodowe - your original family name (before you got married, if you are not married or you didn't change it, and therefore you have never changed your family name, just put here the only one you have ever had)
- Nazwisko... - your current family name
- Imiona - all your "first" names (so not the family name)
- Imię ojca - first name of your father
- Imię matki - first name of your mother
- Data urodzenia - your birth date
- Nazwisko rodowe matki - maiden name of your mother (if she has never changed it, just put the current one)
- Miejsce urodzenia - City, town or village where you were born
- Obywatelstwo - nationality (if you are Japanese, write "japońskie" or: "Japonia")
- Miejsce zamieszkania - your current address where you live
- Wskazanie postępowania... - you may leave it empty, it's needed only if you apply for a certificate for someone else, which is allowed only in special cases
- Rodzaj danych... - you may mark all three points and it's the safest option, it doesn't increase the price
- Zakres danych... - you may leave it empty, reason the same as two fields above
You must transfer 30 PLN to the following bank account:
Recipient: Ministerstwo Sprawiedliwości, Al. Ujazdowskie 11, 00-950 Warszawa
Bank name: NBP O/O Warszawa
IBAN: PL 77 1010 1010 0400 1922 3100 0000
Narodowy Bank Polski
Oddział Okręgowy Warszawa
Plac Powstańców Warszawy 4
The transfer title must contain the same date as in "data wystawienia" on the application form and your name (first name and family name is enough).
and attach the confirmation of the transfer to the application.
Send it to:
Biuro Informacyjne KRK
ul. Czerniakowska 100
They have 7 days to prepare the certificate + the time for the post to deliver it in both directions + 20 days because if you are not a Polish citizen, they are obliged to ask your country if your records are clear also there and your country has 20 days to answer.
So if you need it quickly, try to contact both the Polish institution (Biuro Informacyjne KRK), as well as the institution responsible for issuing such certificates in your country (whom Poland will have to ask), and ask them to do everything quickly. And send it by a possibly fast kind of post service.
The certificate is actually just a stamp on your application. I am not sure how it is if you do it by post, but probably they will just send it back with a stamp.