If your standard deduction is more than your income, in most cases your tax will be zero, and in most cases you are not required to file a tax return. However, you are still required to file a tax return if you had net self-employment income of $400 or more, or if you received Advance Premium Tax Credit for health insurance from the Marketplace ("Obamacare"). There are other less common situations where you might still be required to file. To make sure, go to the following link on the IRS web site.
Do I Need to File a Tax Return?
Even if you are not required to file a tax return, you should file if you had any federal income tax withheld from your pay or other income, in order to get a refund of the tax that was withheld.