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

Yes

The word "leio" (the first-person singular present indicative of the verb ler) has the exact same meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. The only difference lies in pronunciation.

In Brazil, the vowels tend to be more open and the diphthong "ei" is pronounced more clearly and distinctly. In Portugal, vowels are often more "closed" or reduced; the unstressed final "o" in "leio" is often pronounced as a very short, subtle [u] or may even be almost swallowed in rapid, casual speech.

Brazilian Portuguese examples:

1. Eu leio um livro todo mês. (I read a book every month.)
2. Eu leio as notícias no celular. (I read the news on my cell phone.)
3. Eu leio muito antes de dormir. (I read a lot before sleeping.)
4. Eu leio bastante sobre ciência. (I read quite a bit about science.)
5. Sempre leio o que me mandam. (I always read what they send me.)

Continental Portuguese examples:

1. Eu leio um livro todos os meses. (I read a book every month.)
2. Eu leio as notícias no telemóvel. (I read the news on my mobile phone.)
3. Leio sempre antes de dormir. (I always read before sleeping.)
4. Eu leio muito sobre ciência. (I read a lot about science.)
5. Leio o que me enviam. (I read what they send me.)