It's more than a bit possible that OP is worried that if his brother gets married in the US, said marriage won't be recognized by the Muslim religion. OP's brother can "get married in a Muslim way" in the US, but because this is not a legal issue (and therefore appropriate for this forum), OP and/or his brother need to consult with Muslim religious officials in the US to find out how that can be done.
The thing is, any recognized Muslim clergy person should be able to sign the license, the same as for the clergy of any other religion, in order for the license to be valid.
So, the question is, what CT marriage requirement is OP's brother concerned about?
1) Is the bride or groom underage? We are slowly but surely banning child marriage in the US.
2) Are the bride and groom more closely related than 1st cousins? Cousins can marry in CT, but closer than that is incest.
3) Is either party already married? Bigamy is still illegal.
4) Will both parties be present? Proxy marriages aren't a thing here: both parties have to be present.
If OP's brother's issue is that he wants a proxy marriage, where the wife won't be present, then no, that should not be recognized in CT.
That does not mean that he cannot have a proxy marriage. It just means that it will have to be followed up by a legally recognized marriage in order to be recognized in CT. This can be done with any legally recognized officiant. It is a matter of doing the paperwork for the license at town/city hall and getting a signature, and there need not even be a particularly special ceremony associated with the signature.