I started a new business in one state and then moved to another state. My business had no income in 2016. How do I report the loss between the two states?

You have to do an allocation.  So for example, if the business loss is $5K you have to try to determine how much is the first state and allocate reminder to 2nd state. 

There is no formula to do this, you just have to use good judgment and sound logic.