Well, the questionnaire that they provide you to complete (you can find it at their website ...
http://www.ct.gov/bfpe/cwp/view.asp?a=3291&Q=419136) the board is certainly playing games... why do they need to know: your employer , your DMV record, your arrest record etc..
So, how do you want to play the game? The ask many questions that are simply not relevant and ones that can actually cause you harm. The employer one is especially disturbing .. they can contact your employer and tell them you are seeking a permit; your employer is free to terminate you for this reason.
According to Connecticut administrative law:
Sec. 4-178. Contested cases. Evidence. In contested cases: (1) Any oral or documentary evidence may be received, but the agency shall, as a matter of policy, provide for the exclusion of irrelevant, immaterial or unduly repetitious evidence; (2) agencies shall give effect to the rules of privilege recognized by law; (3) when a hearing will be expedited and the interests of the parties will not be prejudiced substantially, any part of the evidence may be received in written form; (4) documentary evidence may be received in the form of copies or excerpts, if the original is not readily available, and upon request, parties and the agency conducting the proceeding shall be given an opportunity to compare the copy with the original; (5) a party and such agency may conduct cross-examinations required for a full and true disclosure of the facts; (6) notice may be taken of judicially cognizable facts and of generally recognized technical or scientific facts within the agency's specialized knowledge; (7) parties shall be notified in a timely manner of any material noticed, including any agency memoranda or data, and they shall be afforded an opportunity to contest the material so noticed; and (8) the agency's experience, technical competence, and specialized knowledge may be used in the evaluation of the evidence.
Are you willing to object to irrelevant questions? Your arrests and DMV record is not relevant as they do not mean anything to your gun rights. But if you do answer and miss a ticket, then you'll be found ineligible due to lying on the form. So, the "game" is the protection of your rights; you willing to fight for them or do you wish to just provide them whatever information they ask from you?
Your employer may not terminate you, I am not trying to scare you but it is a possibility - some employers are anti-gun to this point. I have had employers ask me if I owned guns