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

No.

While the literal meaning (meaning "disconnected," "unplugged," or "turned off") is identical in both dialects, there is a difference in typical usage when describing a person's personality. In Brazil, "desligada" is a very common colloquial way to describe someone who is "spacey," "absent-minded," or "clueless." In Portugal, while "desligada" can be used to describe someone who is "out of touch" with news or social reality, a person is much more likely to use the words "distraída" (distracted) or "desatenta" (inattentive) to describe someone who is forgetful or not paying attention.

Brazilian Portuguese

1. Ela é muito desligada e sempre perde o celular. (She is very absent-minded and always loses her cell phone.)
2. A televisão está desligada. (The television is turned off.)
3. Você está muito desligada hoje, aconteceu algo? (You are very spacey today, did something happen?)
4. A luz da cozinha está desligada. (The kitchen light is turned off.)
5. Ela é tão desligada que nem viu o ônibus chegar. (She is so absent-minded that she didn't even see the bus arrive.)

Continental Portuguese

1. Ela é muito distraída e perde sempre o telemóvel. (She is very distracted and always loses her mobile phone.)
2. A televisão está desligada. (The television is turned off.)
3. Estás muito desatento hoje, aconteceu algo? (You are very inattentive today, did something happen?)
4. A luz da cozinha está desligada. (The kitchen light is turned off.)
5. Ela é tão distraída que nem viu o autocarro chegar. (She is so distracted that she didn't even see the bus arrive.)