Some confusion. When is homeowners insurance a prepaid on the Closing Disclosure?

When they buy insurance to satisfy the conditions of getting the loan, usually on purchase money transactions. In other cases, typically if you are requiring them to pay next year premiums or increase their coverage in connection with the loan.

In a refinance, you might also show it if the annual premium is due prior to the first payment or any monthly payments that might be due if they have their account drafted monthly. Right?

If you are collecting them in connection with the origination of the loan, yes.