My federal refund was returned to the irs for absent name on the checking account. Now what will happen with my state return? Will it also be sent in a paper check form?

For your federal return, a paper check will be mailed to the address on the tax return.  More than likely your state refund will be returned for the same reason and a paper check will be mailed as well. I recommend you be proactive and contact your state department of revenue regarding this issue.  It is likely contacting them will result in your getting your refund sooner.