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

Yes

The word "relatório" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only difference is in pronunciation. In Brazilian Portuguese, the vowels are more open and articulated; for example, the unstressed "e" and "a" are clearly heard. In Continental Portuguese, unstressed vowels are much more closed or "swallowed," making the word sound more clipped and the final "o" sound more like a "u."

Brazilian Portuguese Examples:

1. Eu preciso entregar o relatório amanhã. (I need to hand in the report tomorrow.)
2. O relatório de vendas está pronto. (The sales report is ready.)
3. Você já leu o relatório financeiro? (Have you read the financial report?)
4. O relatório ficou muito detalhado. (The report became very detailed.)
5. Vou revisar o relatório antes da reunião. (I'm going to review the report before the meeting.)

Continental Portuguese Examples:

1. Tenho de entregar o relatório amanhã. (I have to hand in the report tomorrow.)
2. O relatório de vendas está concluído. (The sales report is finished.)
3. Já leste o relatório financeiro? (Have you read the financial report?)
4. O relatório ficou bastante detalhado. (The report became quite detailed.)
5. Vou rever o relatório antes da reunião. (I'm going to review the report before the meeting.)