SHort answer is yes!
Are you on oestrogen as well though or other hRT?
If not on HRT then when you get to menopause oestrogen levels fall dramatically. Testosterone levels fall from some sort of age not sure when - (mid 30's or so maybe) but the drop is gradual. So - when you reach menopause and beyond for a few years you get a relative dominance of testosterone to oestrogen which causes the changes we don;t like to see ie change in body shape from pear to apple shpe (fat round the middle), sometimes a slightly deepened voice compared to when we were younger - you can hear this on the radio, and the awful hairs on chin and lip (as well as reduced body hiar round pubes and pits - the latter I think due to decline in T overall?). It's a very complex issue!!
You don;t actually need T tested if you have low libido, and are not on Anti-deps or taking oral oestrogen then usually low libido while on oestrogen replacement hRT should be sufficient for a doc to prescribe replacement T ( off-licence so may not be possible on NHS). Also some progestogens are androgenic - because they are testosterone derived so can cause the hair issue, but these can also sometimes help to increase libido. T tests are inaccurate for women because they are not sensitive enough in the female range but once T replacement is given then tests should be carried out to ensure levels don't get too high.
Hope this helps - just my thoughts as they came to me and not in any sort of order
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Hurdity x