This has long been a topic of discussion on these threads and I don't believe there is a law that governs this (though someone from OH may be able to chime in and you could check the uniform commercial code).
To me, it is a risk decision. Some banks allow this, but I have seen where banks have had to reimburse a business (the legal entity) for checks they cashed/deposited for individuals who did not own the business and, therefore, did not have a right to the funds. As you can imagine, the risk can elevate extremely quickly if you allow any individual customer to cash/deposit business checks.
That said, if the business is a Sole Proprietor, the individual and "business" are one in the same and, thus, I don't see a problem with this - except that it becomes difficult to differentiate between Sole Proprietors and other entities, meaning it is easier to just draw a line in the sand and say you don't allow this practice.
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Adam Witmer, CRCM
All statements are my opinion, not those of my employer, and should not be taken as legal advice.
www.compliancecohort.com