I am a New York attorney.
A Certificate of Good Conduct or a Certificate of Relief from Civil Disability is designed to prevent employers and licensing agencies from discriminating against a former criminal offender based on his prior criminal convictions. It restores the civil rights he lost as a result of his crime and conviction.
Although you apply for it through the Department of Parole, you need not have ever been on parole or probation to apply for it. The form that the previous professional gave you is, in fact the correct one. This document will explain what the conviction is about and what it can or cannot do for you.
That said, if all that is on your New York record is a traffic infraction, those are not criminal matters,
and a Certificate of Relief or Certificate of Good Conduct would not be something for which you would be eligible. To apply for a Certificate of Good Conduct you need to have been convicted of at least two felonies
. Otherwise, if your convictions are misdemeanors or you have only one felony, you'd get a Certificate of Relief from Civil disabiities.
This is the only Certificate of Good Conduct that the state offers, so it would appear that whoever advised you to obtain one may be in error. Traffic matters do not show up on one's criminal history, unless they are misdemeanors, such as DWI, hit and run, reckless driving and driving on a suspended license.