Can I have an Ohio business with a California address?

You can live wherever you want and have a business wherever you want. Especially with an LLC.

The IRS doesn't care because with an LLC, the profit flows through the business to it's Members, to the extent of their basis. So if you own 75% and another Member owns 25%, then the profits are distributed that way and reported on the "K-1" with the federal return. LLC's pay no federal income tax as it is al allocated to the Members.

The only issue is at the state level wherever you live. If you meet the residency test for that State (which you can find online), then that is where your state taxes - if any - would be calculated and paid based on your K-1 return. You certainly wouldn't want it to appear you have a CA residence with their tax level!

I would suggest that you establish residency wherever you live. I too have a virtual mailbox AND live outside of the country. Doesn't affect my LLC in the states at all.

Feel free to reach out if you need further help.

As long as you pay your taxes, I don't think any government cares. However you are just causing yourself more reporting issues and problems. You have to file corporate paperwork in both states, is it worth the paperwork. Easier to get either a new corp, or a new register agent in location where corp is. Anyway the bigger problem I see is; how do your customers see it, are you losing business because of it, are they thinking your hiding something... I see this all the time with people selling in Florida, but have a Nevada Corp. People don't trust them as much, And isn't sales all about trust.