The short answer: Not without paying federal excise tax and filing federal paperwork. Unlike wine and beer, federal law does not permit the production of distilled spirits for personal or family use.
In order to produce distilled spirits for beverage use or industrial purposes, you must first qualify with TTB under the requirements of the Internal Revenue Code of 1986, and under the Federal Alcohol Administration Act in the event you are producing or bottling distilled spirits for a beverage use. Some of these requirements are:
Paying a special tax
Filing an extensive application
Filing a bond
Providing adequate equipment to measure spirits
Providing suitable tanks and pipelines
Providing a separate building (other than a dwelling)
Maintaining detailed records, and filing reports
All of the requirements are listed in 27 CFR Part 19. There are significant civil sanctions and criminal penalties for the unlawful production of distilled spirits.
In addition, you should check with your state alcohol regulator to determine the applicable state law requirements. A federal qualification to produce distilled spirits does not exempt you from complying with state law requirements.