I have found two papers related to garlic for treating alopecia areata [1,2].
Is there any other evidence for hair growth in androgenetic alopecia?
In fact there are some statements [3,4] that it actually can cause hair loss.
 Hajheydari Z, Jamshidi M, Akbari J, Mohammadpur R. Combination of topical garlic gel and betamethasone valerate cream in the treatment of localized alopecia areata: A double-blind randomized controlled study. Indian J Dermatol Venereol Leprol 2007;73:29-32.
 Sharquie KE, Al-Obaidi HK. Onion juice (Allium cepa L.), a new topical treatment for alopecia areata. J Dermatol 2002 Jun; 29 (6): 343–6
What about the following link: Garlic increases nitric oxide  by Hydrogen Sulfide which it contains . Minoxidil is also related to the generation of nitric oxide through vascular endothelial growth factor (VEGF)  and promotes hair growth. Can garlic have the same or similar or any effects on hair like Minoxidil via nitric oxide?
References:  Messenger, A. G., and J. Rundegren. "Minoxidil: mechanisms of action on hair growth." British journal of dermatology 150.2 (2004): 186-194.
 Ping-Ho Chen, Yaw-Syan Fu, Yun-Ming Wang, Kun-Han Yang, Danny Ling Wang, and Bin Huang, “Hydrogen Sulfide Increases Nitric Oxide Production and Subsequent S-Nitrosylation in Endothelial Cells,” The Scientific World Journal, vol. 2014, Article ID 480387, 8 pages, 2014. doi:10.1155/2014/480387