Relocating to another state with a child. I am divorced with custodial and residential custody.?

My ex-husband doesn't pay his support on time, he waits till the last minute to pay. By that, meaning he had a warrant for his arrest for 6 months and then he paid it in full. I do not know where he got the money, since he has no job. He already lives in another state himself, but i would be moving our child farther away. Our child is 5 and turns 6 in July. I have already notified the courts of my move. They sent him a letter and he called me and told me that he will not allow me to move out of Ohio with his son. He lives in Michigan. Does he have any right to keep me here, even if he attains a lawyer?