In order to get an "earned income" tax credit (for low-income parents of qualified children,if that's what you're asking) you need to have earned SOME income during the year for which you're filing a tax return. In general, people who haven't earned any income aren't eligible. People often have mixed income situations, though (like not working but earning a little or having some other income to report), so without exact details of your situation it's not really possible to give the best answer. Again, though, in general, if there was no work and no earned income at all, no.
The Internal Revenue site offers easy-to-read explanations of different credits, who has to file, etc.; so if you have income you have to report (or a little bit of income you earned and wouldn't be required to report) it might be good for you to go to their site and search their questions feature.