Many species of deer, like the red deer and the white-tailed deer, are considered wild animals and are not allowed to be kept as pets. In general, almost every state in the United States currently prohibits keeping deer. Some states have special permitting and regulations surrounding pet deer, but most are retroactive to deer captured by hand before 2012, effectively grandfathering deer ownership into current laws.
A handful of states have specially written laws related to pet deer. Arkansas and Alabama allow pet deer if the pet was captured by hand before July 2012. Colorado, New Hampshire, and Vermont also allow deer to be kept as pets.
South Dakota has a special set of laws that relate to keeping wild deer. The deer can be used to breed with free-roaming wild elk, sheep, and goats as long as the animals are kept east of the Missouri River. Acceptable deer species that can be used to enhance current free-roaming stock include red deer, sika deer, Sambar, Pere David's deer, and axis deer.
A deer can be kept as a pet in Idaho as long as special permitting is obtained. Florida, Kansas, Michigan, Minnesota, Mississippi, Missouri, New Jersey, North Dakota, Oregon, and Wisconsin also require special permits to keep deer as pets. In Wisconsin, only white-tailed deer are eligible to be kept with a permit.
One of the main reasons pet deer are illegal is that they are extremely dangerous animals. Male deer can get a boost of testosterone during the breeding season. The additional testosterone can make the deer extremely unpredictable and territorial. They are large and powerful animals and can quickly injure or even kill a person.
Deer are also not able to be domesticated. They can be incredibly moody and erratic, making them even more unpredictable. They can jump high, escape enclosures, and be nervous, potentially dying of stress. Plus, deer are not easily harnessed or saddled, so there is no actual use to keep deer as domesticated animals.
As tempting as it may be to take the baby deer home, you should leave the deer be. If you happen to come across a baby deer that appears to be abandoned in the forest, the best thing you can do is to leave the fawn alone. Baby deer don't yet smell, so often, predators don't know they're there. The baby deer have excellent camouflage, so a baby left alone is usually very safe. Chances are, the mother deer has simply stepped away from her baby so that she can eat. Never try to touch or handle the baby deer because this could risk transferring your scent and germs to the fawn.