The law specifies that all taxable personal property must be assessed as of a specific point in time, and that point is precisely at 12:01 a.m. January 1 (regardless of what transpires after that date). Even if closed shortly after the lien date, a business must still file a Business Property Statement and pay taxes for the coming fiscal year on any taxable property they owned on the lien date.
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.
The "mit beschränkter Haftung (mbH)" suffix (German: [ˈɛmbeːˌhaː], "with limited liability") is sometimes added to the name of a firm that already ends in "-gesellschaft" ("company"), e.g., "Mustermann Dental-Handelsgesellschaft mit beschränkter Haftung" ("dental trading company with limited liability"), which would be abbreviated as "Mustermann Dental-Handelsgesellschaft mbH".
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".