Adverse effects of testosterone supplementation may include increased cardiovascular events (including strokes and heart attacks ) and deaths based on three peer-reviewed studies involving men taking testosterone replacement.  In addition, an increase of 30% in deaths and heart attacks in older men has been reported.  Due to an increased incidence of adverse cardiovascular events compared to a placebo group , a Testosterone in Older Men with Mobility Limitations (TOM) trial (a National Institute of Aging randomized trial) was halted early by the Data Safety and Monitoring Committee .  On January 31, 2014, reports of strokes , heart attacks , and deaths in men taking FDA-approved testosterone-replacement led the FDA to announce that it would be investigating the issue.  Later, in September 2014, the FDA announced, as a result of the "potential for adverse cardiovascular outcomes", a review of the appropriateness and safety of Testosterone Replacement Therapy (TRT).    The FDA now requires warnings in the drug labeling of all approved testosterone products regarding deep vein thrombosis and pulmonary embolism . 
Unlike estrogen, androgen levels don't suddenly drop when you reach natural menopause. Instead, androgen production begins slowly falling in your twenties. By the time you reach menopause, you're producing about half as much as you made at puberty. However, your ovaries may still continue to produce small amounts of androgens even after menopause. Some studies show menopausal ovaries continue to produce testosterone; other studies show they do not. One thing is for sure: if your ovaries are removed or damaged, you will go into surgical or early menopause. Some women who experience surgical menopause report a drop in sexual desire and drive.