If you business is a partnership or corporation, then you MUST file a Tax Return for your Business even if there is little or no activity. Partnerships file Form1065, S-Corporation file form 1120-S, and C-Corporations file form 1120.
If you business is a sole proprietorship and you had no income, it may still benefit you to file a Tax Return if you were actively engaged in the business activity and your expenses were ordinary and necessary for the operation of your business. the form you will file in this case will be a Schedule C that will be part of your 1040 (Individual Tax Return).
https://www.irs.gov/faqs/small-business-self-employed-other-business/entities/entities-4
