If my bank routing info is on my Arkansas return and it is not on my Federal return (since I did not get a federal refund), will my stimulus check have to be mailed?

The IRS does not get any information from a State return.  The IRS is setting up a portal soon so you can add direct deposit information.  If you do not have direct deposit information a check will be mailed.

The IRS does not have my direct deposit information. What can I do?

In the coming weeks, Treasury plans to develop a web-based portal for individuals to provide their banking information to the IRS online, so that individuals can receive payments immediately as opposed to checks in the mail.

https://www.irs.gov/newsroom/economic-impact-payments-what-you-need-to-know