Rats https://www.ncbi.nlm.nih.gov/pubmed/2821655
Humans and Rats https://www.ncbi.nlm.nih.gov/pubmed/6816576
Nested case control study? https://www.ncbi.nlm.nih.gov/pubmed/11170129
Vitamin E related to slightly lower testosterone. Need to look into methodology in more detail.
Observational study: In smokers there is an inverse correlation between serum α-tocopherol and sex steroid hormones
https://www.ncbi.nlm.nih.gov/pubmed/21424597
Observational study: Infertile men have lower levels of Vitamin E compared to fertile men
https://www.ncbi.nlm.nih.gov/pubmed/22818093
Rat study:
https://www.ncbi.nlm.nih.gov/pubmed/2821655
Vitamin E deficiency reduces testosterone, and slightly elevates LH. This suggests it is working at a testicular level - although perhaps not exclusively. The formation of cAMP also decreased significantly in the Vitamin E group.
Rat study:
https://www.ncbi.nlm.nih.gov/pubmed/3012051
Vitamin E deficiency reduces testosterone, but leaves LH unchanged (surely it should go up if this problem was purely testicular in nature). Administration of DPPD (an antioxidant which has shown to be active in the testes - see https://www.ncbi.nlm.nih.gov/pubmed/21310208) seemed to reverse the change - so the problem may not be low vitamin E, it might be low levels of antioxidants active in the testes.