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

Yes

The word "dormiu" is the third-person singular of the verb dormir in the pretérito perfeito do indicativo (simple past). There are no differences in meaning, spelling, or grammatical function between Brazilian and Continental Portuguese. The only differences are phonetic, specifically regarding the cadence, the reduction of unstressed vowels, and the specific pronunciation of the vowels in different regional accents.

Brazilian Portuguese Examples

1. Ele dormiu muito tarde hoje. (He slept very late today.)
2. O cachorro dormiu no tapete. (The dog slept on the rug.)
3. A criança dormiu o dia todo. (The child slept all day.)
4. Você viu que ele dormiu no ônibus? (Did you see that he slept on the bus?)
5. Ela dormiu sem nem tomar o remédio. (She slept without even taking the medicine.)

Portuguese (Portugal) Examples

1. Ele dormiu muito tarde hoje. (He slept very late today.)
2. O cão dormiu no tapete. (The dog slept on the rug.)
3. A criança dormiu o dia inteiro. (The child slept the whole day.)
4. Reparaste que ele dormiu no autocarro? (Did you notice that he slept on the bus?)
5. Ela dormiu sem sequer tomar o medicamento. (She slept without even taking the medication.)