In this case, you need to write a remark about that circumstance on the Business Property Statement, or on an attachment to it. Also fill out Part III (Equipment Belonging To Others) of the form. If you own any small equipment, such as a printer, copier, etc., that you are using in the business, you should report these costs under Part II of the Business Property Statement and also Schedule A.
A grocery store goes out of business prior to January 1st but equipment such as freezer boxes and store shelving remains in the building on that date. In this case, such items would still be taxable and must be reported even though the business was closed on the Lien Date. That is because in this case, the equipment could not revert to or be used as "Household Furnishings or Personal Effects".