“A lives in New York, and B lives in London. Car C and car D are belong to them respectively.”
According to this paragraph, Car C belongs to A, not B, because A is mentioned earlier than B, or it doesn’t matter whether Car C belongs to A or B because the order is determined in the sentence, not the other sentences.
“A lives in New York, and B lives in London. Car C and car D belong to them respectively.”
This means that Car C belongs to 'A', and car D belongs to 'B'.
This is because person A and B were listed in that order, and cars C and D were listed in that order.
'Respectively' means that the previously used order is being reused and applies to the second list.
Your example is odd. If we fix the grammatical error, it still seems awkward. The sequence referred to occurs in one sentence, and the referring “respectively” occurs in a different sentence.
A lives in New York, and B lives in London. Car C and Car D belong to them respectively.
I’ll not go so far as to say that the use of “respectively” here is an error in grammar, but it certainly is not idiomatic.
A, who lives in New York, owns a BMW whereas B, who lives in London, owns a Rolls Royce.
The point, I think, is that “respectively” has a limited use and is seldom used to reference an order listed in a separate sentence.
