When Social Security is the only source of income for your entire household, no tax return needs to even be filed at all. But when you have other income, such as your part time income in 2015, and that income is more than $6200, then a tax return is required to be filed.
If the taxable income reported to you on a W-2 is less than $6200, then a tax return does not need to be filed. HOWEVER, if any taxes were withheld on those earnings, then you should file a tax return anyway so those withheld taxes can be refunded to you.
If you have income of over $400 that is reported to you on a 1099-MISC in box 3 or 7, and/or self-employment income, then you are required to file a tax return.
For either scenario above, you will also report your SS income. Generally, the SS income will still not be taxable provided your earned income is below a certain thresh hold as identified at https://www.ssa.gov/planners/taxes.html
