There is no such thing as a minimum. If you were "open for business" for even one day in the tax year, then you are required to file a tax return. Even if that business has zero income and zero expenses. Also, you are required to claim all business expenses weather you want to or not. Even if your expenses exceed your business income, you must still report all of them.
Basically, once your deductible business expenses get your taxable business income to zero, that's it. Any remaining expenses are just carried forward to the next year where they are deducted, if the business has the income to deduct them from. In some cases, the excess business expenses can be claimed against other ordinary income (such as W-2 income) thus further reducing your taxable income for the tax year.
