Do you mean Muslims living in the crusader states? If so, there were no special arrangements…the crusaders had no interest whatsoever in the social lives of the Muslims (or Jews, or eastern Christians) who lived there.

Some things did change - Muslims now had to pay the same taxes that social-minority populations used to have to pay to them. They could also be enslaved, and they might be randomly harassed by whoever the local crusader lord was. But generally the crusaders left them alone and they could continue to live as they had before. They didn’t have to seek permission to marry from crusader authorities, religious or secular.

Perhaps someone with more expertise in Islamic law can help with this part, but there aren’t really “religious authorities” in Islam in the same way there are/were in Christian countries. There’s no separation of church and state; there wasn’t much separation between the two in medieval Christian territories either, but there was a distinction between the Roman church and the Roman Empire. Islamic countries didn’t have that - everything was religious (or, maybe, equally religious and equally secular at the same time).

A Christian couple would be married in a church by a priest and their lives would be determined by religious law in some ways - sexual matters, raising children, and ending the marriage if necessary; and secular law in others - especially the way that property could be shared or inherited by a spouse or their children.

For Muslim couples, their marriage would be more like any other contract. Both the husband and wife had to consent (or their families would come to an agreement for them) and there would probably be a ceremony to celebrate, but it didn’t have to involve a religious building or a religious authority. If there were any disputes in the marriage afterwards, about marital issues or property or anything else, they could consult an Islamic judge (the local qadi). Since there was no church-state distinction and no separate secular and religious courts, all issues would be decided in a single court that dealt with both kinds of matters.

The only time crusader authorities in the Levant might take notice of a wedding was if a Latin Christian (a member of the Roman church) married a Muslim. That would be extremely unusual and, according to the Roman church, such a marriage would be invalid because a Latin Christian would not be allowed to marry a non-Christian. But apparently it sometimes happened anyway, and the secular court in the crusader legal system might get involved in there were issues of property inheritance - could a non-Christian spouse inherit the property of their deceased Christian spouse? If they had children, could they inherit property? The secular courts seem to have accepted that a Christian and non-Christian could be married (the marriage was not invalid), but they disagreed on the legal ramifications of the marriage (the marriage might be illicit).

Otherwise, aside from these apparently extremely rare situation, Muslims could freely marry other Muslims according to whatever customs they had before. The crusader authorities were not interested in their daily lives at all. Hopefully that helps...sorry if I misunderstood your question and this isn't what you were asking about!

Sources:

James A. Brundage, "Marriage law in the Latin Kingdom of Jerusalem", in Outremer: Studies in the History of the Crusading Kingdom of Jerusalem, ed. B. Kedar, H. Mayer, R. Smail (Jerusalem, 1982)

Marwan Nader, "Urban Muslims, Latin laws, and legal institutions in the Kingdom of Jerusalem", in Medieval Encounters 13 (2007)

Hans E. Mayer, “Latins, Muslims, and Greeks in the Latin Kingdom of Jerusalem”, in History 63 (1978)