The basic problem here is that scientific study of cultures (Sociology, Anthropology, etc.) is a relatively new discipline. There are indigenous social scientists today of course (my little sister is one of them), but by the 20th Century a lot of the original beliefs had been lost and a new hybrid culture developed (a process she calls colonial entanglement).
The first indigenous North American I am aware of who endeavored to record native cultures in serious detail was Francis La Flesche, who grew up on the Omaha reservation, and wrote extensive studies of the Omaha and Osage cultures and language at the beginning of the 20th Century. In a lot of ways his timing was fortuitous, because those cultures were newly Christianized, so he was able to get information on a lot of "secret" religious rites while the elders that knew of them were still alive, but after the taboos about sharing them had disappeared.
Both languages are in the same language subfamily as Crow, which tends to be predictive of a lot of other cultural similarities as well, so La Fleche's work is likely to be the best objective window into "Western Siouxan" (including Crow) culture available to you.
I can tell you from what I've researched (I have 2 of La Fleche's works, and have done some other research as well), that all Siouxans I've looked at believed in an omnipresent divine spirit, similar to The Force in Star Wars1, called some variation of "Wakonda"2. Christians like to translate that word to Great Spirit, which is why you see a lot of native-themed "Great Spirit" tchotchkes with what look a lot like Christian homilies on them floating around US tourist traps in the interior of the country.3
A better translation is usually "Great Mystery", but IMHO its probably better to think of it as The Force, but call it by its proper native name (in the language of your choice).
The Osages were divided up into 2 moieties (representing the Earth and the Sky) with 7 clans each (named for what you might call totem creatures, or sometimes just thematically). According to La Fleshe each clan had a part of required rituals they were the secret keeper for, which had a practical effect that major rituals (eg: declaring war) required at least some members of every clan in the entire tribe to gather to carry out properly.
The clan names used vary quite a bit by culture, but every Siouxan nation I've looked at (and many non-Siouxan) had one for Thunderbird and one for Underwater Panther. They are traditional antagonists, and with the Osages at least are in opposite moieties.
1 - This is not entirely coincidental. This is a common mode of belief not only in North America, but in Asia, and George Lucas according to some sources patterned his fictional "Jedi" religion after it.
2 - As near as I've been able to determine, the similarity to the name of Marvel's fictional African nation is entirely conincidental.
3 - To be fair, my Osage grandfather had one of those hanging framed in his house. So Native Americans themselves actually put stock in these, but that doesn't change the fact that they are modern anachronisms, and usually not genuine pre-contact native wisdom.