If your property is in Arkansas you should register an LLC for this property and only this property in Arkansas. If you buy more properties in Arkansas have each one owned by a separate LLC. Thats the correct way to do it and here is why:
1) if something happens (a tenant in this property is suing you) and you have this property owned in some LLC with other properties you are exposing those other properties to be affected by the results of the litigation (in other words its a choice of possible loosing one vs. possibly loosing all)
2) if you own all your properties by lets say a Wyoming LLC (which is one of the best states to have your company registered in, but still) you will need to form a Foreign Entity of that LLC in Arkansas. If you do you end up, again, owning all your properties in that state by one entity.
So whats the solution? Have your main "holding" (or "management", if you prefer) company organized in let's say Wyoming, and let this Wyoming company own all of those local LLCs that will hold your investment properties.
Of course, the problem is what if you have 100 properties? Yes, you do need 100 LLC – except in few states that have what is called a Series LLC. Only few states do, those states are Delaware, Nevada, Illinois, Iowa, Tennessee, Oklahoma, Texas, Utah and Wisconsin. When you own properties in those states you can have them all owned by one entity, the series LLC, yet put each one in a separate series, thus protecting each property from the other, while saving money and trouble registering and managing LLC for each one.
Hope thats helpful.