Does TSH and Growth hormone have any role in menstruation?
TSH has an effect slightly similar to that of FSH and LH. This is found to be problematic in thyroid diorders. For example, in hypothyroidism the TSH overflow causes children to become fertile at an earlier stage, compared to the norm [1].

[1] Ann N Y Acad Sci. 1997 Jun 17;816:280-4. PMID: 9238278. http://www.ncbi.nlm.nih.gov/pubmed/9238278