From the Kentucky State Police website:
The applicant for a carry concealed deadly weapon (CCDW) license must:
Be a resident of Kentucky for at least six months prior to filing the application or a member of the Armed Forces of the United States who is on active duty, who is at the time of application assigned to a military posting in Kentucky, and who has been assigned to a posting in Kentucky for six months or longer immediately preceding the filing of the application; and
Be twenty-one (21) years of age or older; and
Not be under indictment for, or have been convicted of, a crime punishable by imprisonment for a term exceeding one year; and
Not be a fugitive from justice; and
Not be an unlawful user of or addicted to any controlled substance; and
Not have been adjudicated as a mental defective or have committed to a mental institution; and
Not have been discharged from the Armed Forces under dishonorable conditions; and
Not be subject to a domestic violence order or emergency protective order; and
Not have been convicted of a misdemeanor crime of domestic violence (see section below for discussion of misdemeanor crimes of domestic violence); and
Not be prohibited from the purchase, receipt or possession of firearms, ammunition or both pursuant to 18 U.S.C. 922(g), 18 U.S.C. 922(n), or applicable state law; and
Not have been committed to a state or federal facility for abuse of a controlled substance or convicted of a misdemeanor relating to a controlled substance within the three-year period immediately preceding the date the application was submitted; and
Not have two or more convictions for violating KRS 189A.010 (Operating motor vehicle under the influence of alcohol or other substance which impairs driving ability) within the three (3) years immediately preceding the date on which the application is submitted; and
Not have been committed as an alcoholic pursuant to KRS Chapter 222 or similar laws of another state within the three (3) year period immediately preceding the date on which the application is submitted; and
Not owe a child support arrearage which equals or exceeds the cumulative amount which would be owed after one (1) year of nonpayment; and
Have complied with any subpoena or warrant relating to child support or paternity proceedings; and
Have not been convicted of a violation of KRS 508.030 (Assault in the fourth degree) or 508.080 (Terroristic Threatening in the third degree) within the three years immediately preceding the date on which the application is submitted; and
Demonstrate competence with a firearm by successful completion of a firearms safety or training course offered or approved by the Department of Criminal Justice Training.