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 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.
On the other hand, if you are not responsible for its tax, then you should declare the equipment in Part III of the Business Property Statement (Equipment belonging to others). Where equipment is declared in Part III of the Business Property Statement, the Assessor will also send a Notice to File to the person reported as the equipment's actual owner.