Public property owned by any public agency and in use in the performance of a public function shall not be subject to assessment under this part unless the resolution of intention expressly provides that it shall be assessed. If the resolution provides that public property shall be assessed, the local agency conducting the proceedings shall be liable for payment of all amounts so assessed. Any such amounts shall be payable from the general fund of the local agency unless the resolution of intention designates some other fund. To the extent that any such amounts are paid by the public agency owning the public property, the local agency conducting the proceedings shall not be liable therefor.