Is the word sei the same in Brazilian and European Portuguese?

Yes

The word sei is identical in both Brazilian and Continental Portuguese. There are no differences in its meaning (it is the first-person singular present indicative of the verb saber), its spelling, or its grammatical function. The only differences between the two dialects are phonetic, specifically regarding the intensity of the nasalization of the diphthong and the way the word is integrated into the phonetic rhythm of the surrounding sentence (vowel reduction).

Brazilian Portuguese Examples

1. Eu não sei o que aconteceu. (I don't know what happened.)
2. Não sei se você vem para a festa. (I don't know if you are coming to the party.)
3. Eu sei que você gosta de chocolate. (I know that you like chocolate.)
4. Não sei se a gente vai sair hoje. (I don't know if we are going out today.)
5. Eu sei, mas não conto para ninguém. (I know, but I won't tell anyone.)

Portuguese (Continental) Examples

1. Não sei o que aconteceu. (I don't know what happened.)
2. Não sei se tu vens para a festa. (I don't know if you are coming to the/the party.)
3. Sei que tu gostas de chocolate. (I know that you like chocolate.)
4. Não sei se vamos sair hoje. (I don't know if we are going out today.)
5. Sei, mas não conto a ninguém. (I know, but I won't tell anyone.)