You have 180 days from the date of the adverse employment action to file a discrimination complaint with the CHRO. Your complaint with the EEOC covers federal law not state law. You should seek an attorney now. Depending on the case and the client's situation, an attorney may be prepared to take the case without a retainer.
Some attorneys require payment on an hourly basis. Some work on a contingency fee basis. The EEOC, under a work sharing agreement with Connecticut, delegates the investigation of federal claims generally to the CHRO. So even though you can assert federal and state claims with the CHRO and EEOC, generally the CHRO alone will investigate the complaint. As the previously poster indicated, make sure you do so in a timely fashion. Although complaints can be filed without the assistance of an attorney, an attorney often can assist you in writing a much stronger complaint by explaining the law and helping you emphasize what is most important to your claim legally and factually.