When it comes to connections with animals the pre-columbian natives of the plains and eastern forests are a good place to start. As for astronomy, the Aztecs, Mayans, and Olmecs would be a great source to look at--especially the Aztec and Mayan.
This being said all native cultures had some association with astronomy. For example, the symbol of the Cheyenne is the Morning Star and their lodges were always set up to face that star's first point of rising. The Navajo also had a strong affinity for both animal/human interaction and for astronomy.
Some places to start looking for information would be the Plains Indian Sun dance, medicine lodge, and sweat lodge. For some tribes these last two are the same, but for others, like the Cheyenne, the medicine lodge was a special tipi set up by the Hat-keeper (Northern Cheyenne) to keep the sacred buffalo hat or the Arrow Keeper (Southern Cheyenne) to keep the sacred arrows.
Also check out the Southwestern native concept of the Thunderbird and their varous seasonal dances.
Keep in mind that many native traditions are not as ancient as they may claim. For example the Cheyenne sundance is only about 175 years old, being received from Erect Horns
after they moved onto the plains where they were driven by other tribes that had traded for guns from the French and British. It is still purely native, but is not that ancient. How much of it is a reaction to white expansion is hard to say. The fertility element in it shows it was created at a time when tey feared the extinction of their tribe.
One good place to start that will give you a good overview of the Cheyenne and some helpful information on the other tribes they interacted with like the Arapahoe and the Kiowa is the book Sweet Medicine. I believe it is published by the University of Oklahoma and I have found it before on Amazon.
Other information to look up is the history of the Black Hills. Some of the myths surrounding Devil's Tower in Wyoming will also show you some of the astronomical and animal elements of their religions.
Keep in mind though the tribes all had different religions and very different concepts of God. Though the push today is for syncretism and claiming that all religions (native and Christian) are ultimately the same and derive from the same place, this was not traditionally believed. Practicing henotheism, each tribe believed their religion was theirs alone. They also judged other religions. For example the Cheyenne saw the Aztec practice of human sacrifice as evil, even though they had their own version of human sacrifice.