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 a few states, you must take an additional step to make your company official: You must publish a simple notice in a local newspaper, stating that you intend to form an LLC. You are required to publish the notice several times over a period of weeks and then submit an "affidavit of publication" to the LLC filing office. Your local newspaper should be able to help you with this filing.