There is no law or regulation that controls this, just your bank's comprehension of and appetite for the risks involved.
The simplest rule is any transfer must be between accounts owned in the same right and capacity; e.g. I can transfer between the accounts I own individually. If the LLC in which I am a member has provided an authenticated resolution indicating I can transfer funds between accounts that it owns, then I can. Those two circumstances in unison do not imply I can transfer from the LLC to my account or from my account to the LLC.