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

Yes

The meaning, spelling, and grammar of "tímido" are identical in both Brazilian and Continental Portuguese. The only differences lie in pronunciation:

• Brazilian Portuguese: The vowels are generally more open and "musical." In many regions of Brazil (such as Rio de Janeiro or São Paulo), the "d" may be palatalized, sounding slightly like a "dj" ([dʒ]). The final "o" is typically pronounced as a soft "u" ([u]).
• Continental Portuguese: The vowels are much more closed and reduced, especially in unstressed syllables. The "d" remains a dental sound ([d]), and the rhythm of the speech is more stress-timed, making the word sound shorter and more clipped.

Brazilian Portuguese Examples

1. Eu era muito tímido na escola. (I was very shy at school.)
2. Ele é meio tímido para chegar nas pessoas. (He is a bit shy when approaching people.)
3. Não seja tímido, participe da conversa! (Don't be shy, participate in the conversation!)
4. A menina ficou tímida com o elogio. (The girl became shy with the compliment.)
5. Você é tímido ou apenas reservado? (Are you shy or just reserved?)

Continental Portuguese Examples

1. Eu era muito tímido na escola. (I was very shy at school.)
2. Ele é um pouco tímido ao falar com desconhecidos. (He is a bit shy when speaking to strangers.)
3. Não sejas tímido, participa na conversa! (Don't be shy, participate in the conversation!)
4. A rapariga ficou tímida com o elogio. (The girl became shy with the compliment.)
5. Tu és tímido ou apenas reservado? (Are you shy or just reserved?)