Menopause can cause hair loss in those predisposed to the condition.
More Info: Although as many as one in two women experience hair loss during menopause, it is important to understand their potential predisposition to this symptom. Even before the onset of menopause, up to 12% of women between the ages of 20-29 have been shown to have some sort of degree of hair loss caused by androgenetic alopecia, which is tied to the body’s hormone levels. 
What Is Androgenetic Alopecia?
Androgenetic alopecia is the principal cause of male pattern baldness, and clinical work has shown that following menopause, women may also be naturally much more susceptible to this problem than previously thought.  By the time women reach the age of 65, as many as 50-75% of them will be affected by this type of hair loss. 
Who Is Susceptible to Androgenetic Alopecia?
It all starts with the enzyme known as 5-alpha reductase. This component creates androgens, which in turn produce a chemical called dihydrotestosterone, or DHT. People whose bodies have more of the 5-alpha enzyme create larger quantities of the DHT chemical, which attacks hair follicles and causes individual hairs to eventually fall out. 
Research Concerning Menopause and Hair Loss
As scientists have delved further into the phenomenon of female hair loss during menopause, the explanations have become both more precise and more challenging. In one case, researchers identified a new gene, ESR2, which was present in cases of severe female hair loss. The findings also determined that what was previously thought to be a good guard against hair loss, the intake of additional estrogen, now appears to be something that would only further feed the gene. These conclusions were drawn from the analysis of 500 women suffering severe hair loss of 50% or more. Ultimately, the connection between menopause and female hair loss grows more tenuous with each additional piece of research, suggesting that not all contributing factors have heretofore been properly categorized and identified. 
 Investig Dermatol Symp Proc.; Gan DC
Prevalence of Male and Female Pattern Hair Loss in Maryborough
2005; Volume: 10; Pages 184-189
 Genetics Home Reference
University of California Berkley-Wellness Alert
Hair-Raising Questions for Women
 Clinical Interventions in Aging; Quan Q Dihn
Female Pattern Hair Loss: Current Treatment Concepts
2007; Volume: 2; No: 2; Pages: 189-199
 British Journal of Dermatology; Yip L
Gene-wide Association Study Between the Aromatase Gene (CYP19A1) and Female Pattern Hair Loss
2009; Volume: 161; Pages 289-294
Glossary of Terms
Androgens: the 19-carbon steroids synthesized by the adrenal cortex that function as weak steroids or steroid precursors.
Dorland’s Medical Dictionary for Health Consumers
Alopecia: the loss of hair.
“he medical name for this is androgenetic alopecia. This condition begins with gradual thinning at the part line. Then comes diffuse hair loss, starting with hairs that come out of the top of the head. Female-pattern hair loss is not like male-pattern balding: A woman’s hairline rarely recedes, and women rarely become bald.”
Dr Anthony Komaroff What Causes Hair Loss in Women?