multi state or multistate or multi-state
I prefer option (1), and cite Donald Knuth's reasoning as given here. 

Knuth asserts that hyphenated versions of "newly coined" words morph to unhyphenated versions (e-mail becomes email, for example) as they gain acceptance and are more frequently used, which indicates to me that option (2) is not off the table, certainly because the word is not newly coined. 

However, I argue that wide acceptance and usage of the wording in the context given here is not demonstrated and fall back to option (1). Finally, as pointed out by Martin in the comment thread, be consistent and use (or don't use) hyphenation regardless of which variation you choose.