Your CPA can advise you better, but basically, no.
You will need to track your expenses and income for the rental property, but nowhere is there a requirement to keep a separate account. If you are holding funds in trust for someone, then you will need a separate account, unless the agreement (typically a lease) states otherwise.
A common mistake is for landlords to spend the security deposit they receive and then when the renter moves out, they try to think up reasons not to return the money. This is a mistake. Keep the deposit in your accounts but do not spend it. You may need it for expenses, and you may need to return it legitimately at the end of the lease.