First, a moment of perspective (from the United States):

Overall, the number of Americans on medications used to treat psychological and behavioral disorders has substantially increased since 2001; more than one ‐ in ‐ five adults was on at least one of these medications in 2010, up 22 percent from ten years earlier. Women are far more likely to take a drug to treat a mental health condition than men, with more than a quarter of the adult female population on these drugs in 2010 as compared to 15 percent of men. Women ages 45 and older showed the highest use of these drugs overall. Yet surprisingly, it was younger men (ages 20 to 44) who experienced the greatest increase in their numbers, rising 43 percent from 2001 to 2010.

And from page 6 of the same report,

An estimated 40 million American adults suffer from anxiety disorders.

Still using 2010 data, that would be about 17% (just over 1/6) of the US adult population. So while issues with depression and/or anxiety can be very significant - and present in variegated forms - they are also not rare. I think this is important to keep in mind when dating. Without getting too caught up in the specific numerics, a number like 1/6 means (roughly) that if you see two couples out on a double date, then chances are at least one of the four people has an anxiety disorder.

Anyway: To respond to your question, I think that you can just tell the person whenever you are comfortable. This may seem like a vague answer, but I think it is correct. If you will insist on a rule of thumb (not a rule in stone!): I think that if you are looking for a relationship and have significant mental health issues, then it is wise to tell them before it becomes romantically physical.

Lastly, bearing in mind the prevalence mentioned above: If you engage in a serious conversation of this manner, do be prepared for the other person to react in a variety of ways. It could be that they need time to process the information; it could be that they react adversely; it could be that they share personal information of a similar nature.