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

Yes.

The word perna is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only difference is in pronunciation:

• Brazilian Portuguese: The vowels are more open, and the unstressed "a" at the end of the word is clearly articulated.
• Continental Portuguese: Unstressed vowels are heavily reduced or "swallowed." The "a" in perna is much more closed and sounds almost like a very short, neutral "uh" or is nearly silent.

Brazilian Portuguese Examples

1. Minha perna está doendo muito. (My leg is hurting a lot.)
2. Ele quebrou a perna jogando futebol. (He broke his leg playing soccer.)
3. Ela tem pernas muito longas. (She has very long legs.)
4. Senti uma dor na perna esquerda. (I felt a pain in my left leg.)
5. Ele deu um chute na minha perna. (He kicked my leg.)

Continental Portuguese Examples

1. A minha perna está a doer muito. (My leg is hurting a lot.)
2. Ele partiu a perna a jogar futebol. (He broke his leg playing soccer.)
3. Ela tem as pernas muito compridas. (She has very long legs.)
4. Senti uma dor na perna esquerda. (I felt a pain in my left leg.)
5. Ele deu um pontapé na minha perna. (He kicked my leg.)