It's all in the regs -
(b) Individuals seeking unescorted access authority. ... each airport operator must ensure that no individual is granted unescorted access authority unless the individual has undergone a fingerprint-based CHRC that does not disclose that he or she has a disqualifying criminal offense, as described in paragraph (d) of this section.
(c) ....
(d) Disqualifying criminal offenses. An individual has a
disqualifying criminal offense if the individual has been convicted, or
found not guilty of by reason of insanity, of any of the disqualifying
crimes listed in this paragraph (d) in any jurisdiction during the 10
years before the date of the individual's application for unescorted
access authority, or while the individual has unescorted access
authority. The disqualifying criminal offenses are as follows--
(1) Forgery of certificates, false marking of aircraft, and other
aircraft registration violation; 49 U.S.C. 46306.
(2) Interference with air navigation; 49 U.S.C. 46308.
(3) Improper transportation of a hazardous material; 49 U.S.C.
46312.
(4) Aircraft piracy; 49 U.S.C. 46502.
(5) Interference with flight crew members or flight attendants; 49
U.S.C. 46504.
(6) Commission of certain crimes aboard aircraft in flight; 49
U.S.C. 46506.
(7) Carrying a weapon or explosive aboard aircraft; 49 U.S.C. 46505.
(8) Conveying false information and threats; 49 U.S.C. 46507.
(9) Aircraft piracy outside the special aircraft jurisdiction of the
United States; 49 U.S.C. 46502(b).
(10) Lighting violations involving transporting controlled
substances; 49 U.S.C. 46315.
(11) Unlawful entry into an aircraft or airport area that serves air
carriers or foreign air carriers contrary to established security
requirements; 49 U.S.C. 46314.
(12) Destruction of an aircraft or aircraft facility; 18 U.S.C. 32.
(13) Murder.
(14) Assault with intent to murder.
(15) Espionage.
(16) Sedition.
(17) Kidnapping or hostage taking.
(18) Treason.
(19) Rape or aggravated sexual abuse.
(20) Unlawful possession, use, sale, distribution, or manufacture of
an explosive or weapon.
(21) Extortion.
(22) Armed or felony unarmed robbery.
(23) Distribution of, or intent to distribute, a controlled
substance.
(24) Felony arson.
(25) Felony involving a threat.
(26) Felony involving--
(i) Willful destruction of property;
(ii) Importation or manufacture of a controlled substance;
(iii) Burglary;
(iv) Theft;
(v) Dishonesty, fraud, or misrepresentation;
(vi) Possession or distribution of stolen property;
(vii) Aggravated assault;
(viii) Bribery; or
(ix) Illegal possession of a controlled substance punishable by a
maximum term of imprisonment of more than 1 year.
(27) Violence at international airports; 18 U.S.C. 37.
(28) Conspiracy or attempt to commit any of the criminal acts listed
in this paragraph (d).