NGB Form 3621 at a glance
What it is: NGB FORM 3621 is the ANG Eligibility Checklist for Enlistment, Reenlistment, or Extension.
Who signs: The applicant signs on the SIGNATURE line, and a WITNESS signs on the witness SIGNATURE line of Section IV with this certification: "I certify the above individual signed this certificate of his/her own free will."
A filled-in NGB Form 3621 example: an applicant signs the checklist

How to fill out NGB Form 3621, box by box
I. For all applicants
Initial YES / NO / N/A boxes as applicable. Provide explanation in comments section for any "YES" responses.
I. FOR ALL APPLICANTS: YES NO N/A Are you a conscientious objector? Are you a sole survivor? If you are an immigrant alien who enlisted on or after 1 June 1983, have you since that time acquired U.S. citizenship status? Are you currently enrolled in the advanced course of Air Force ROTC, Army ROTC, or Naval ROTC, or are you a scholarship student in these programs? Have you engaged in any act(s) designed to destroy or weaken the U.S.? Are you under investigation by military or civilian authorities? Are you an alcoholic? Have you ever been enrolled in a drug and/or alcohol rehabilitation program? Do you have a history of mental illness or emotional instability?
II. For enlistment only
II. FOR ENLISTMENT ONLY: Have you ever been charged, arrested, cited, or convicted for any violation of civil or military law, including non-judicial punishment pursuant to Article 15 of the Uniform Code of Military Justice (UCMJ) or minor traffic violations? Have you ever been separated or are you pending separation from any branch of the uniformed services? Have you ever served in the armed forces of another country? Have you ever served in the Peace Corps? Have you ever tested positive for an illegal drug/substance? Do you have any tattoos, brands, or body alterations/modifications?
III. For reenlistment or extension only
III. FOR REENLISTMENT OR EXTENSION ONLY: Have you ever been charged, arrested, cited, or convicted for violation of any federal, state, or municipal law, to include minor traffic violations during your current Term of Enlistment/Extension? Have you ever been charged arrested, cited, or convicted for violation of any military laws, including non-judicial punishment pursuant to Article 15 of the UCMJ during your current Term of Enlistment/Extension?
Signing and recertification

"I certify that all information contained above is true and current as of the date of my below signature."
I further understand that I must recertify this form to be accurate as of the date of recertification.
Any changes from the current answers will be brought to the attention of my service's Force Support Squadron.
V. RECERTIFICATION AT TIME OF ENLISTMENT, REENLISTMENT, OR EXTENSION: I hereby state that there has been no change in my status since I originally provided this information.
More rules for NGB Form 3621
The form will provide field recruiters a tool to process prospective Air National Guard applicants and analyze pre-enlistment job cancellations for common reasons.
Voluntary. However, failure to provide the requested information will result in disqualification from enlistment, reenlistment, or extension of enlistment in the Air National Guard.
Giving false or misleading information may result in separation from the Air National Guard of the United States.
The proponent agency is NGB/A1PP. The prescribing directive is ANGI 36-2002.
Sources
[1] NGB Form 3621 (20121002), ANG Eligibility Checklist for Enlistment, Reenlistment, or Extension, National Guard Bureau (the Official source link on this page).
