Can a blood test detect 1mg Finasteride? How long before Finasteride no longer shows up in a blood test?

Finasteride is not something blood is tested for.  However, it is never a good idea to withhold information from your primary physician about prescription medications you are taking. 

Finasteride is not something that is tested for. It can affect several blood tests including DHT, PSA, estrogen. But these are not typically screened in routine tests nor are the changes likely to raise concern in a young male if there is no baseline of comparison. While there are many risks in withholding information from a physician, it is not likely that he or she can determine if you are on it or not. Should you wish to stop, it could affect the hair, but most changes would revert quickly in a matter of days. The drug itself is out of the body in just a few days on account of its short half life; changes in DHT PSA take a bit longer to revert.

Finasteride is not something physicians look for in general physicals. In fact I cannot conceive any discipline in medicine where finasteride is a drug to be tested. You should be fine by continuing your hairloss regimen. Also I do not know of any cross reaction of finasteride cross reactivity or mimicking other medications that are tested. However, it can change your PSA or Prostate Specific Antigen that are apart of physicals of men over 40 in the US. So you might want  to tell your doctor if you are of age to be testing your prostate.

The drug finasteride has a half life of about 6 hours, so smaller and smaller amount remain for days possibly even week after stopping the drug. Tissue levels are maintained for 3-4 weeks

A blood test will not test for levels of Finasteride, however, it is important that you are open with your doctor about all of your health issues and especially all medications.