Do you have to file a CT state return for income of $3000?

When I looked at state of Connecticut, it seems to be say no as far as income and yes for these reasons: http://www.ct.gov/drs/cwp/view.asp?a=1462&q=499520

Who Is Required to File a Connecticut Return?

You must file a Connecticut resident income tax return if you were a resident for the entire year and any of the following is true for the taxable year:

•     You had Connecticut income tax withheld;
      You made estimated tax payments to Connecticut or a payment with Form CT-1040 EXT;
      You meet the Gross Income Test;
      You had a federal alternative minimum tax liability; or
      You are claiming the Connecticut earned income tax credit (CT EITC).

As far as income:

You must file a Connecticut income tax return if your gross income for the taxable year exceeds:

    $12,000 and you are married filing separately;
    $15,000 and you are filing single;
    $19,000 and you are filing head of household; or
    $24,000 and you are married filing jointly or qualifying widow(er) with dependent child.

Please look at that link above, and determine what is your situation, since I do not your whole situation.