"At that date" and "on that date" are essentially synonymous. Both can be used for either the future or the past.

"On that date" is the usual version in the US. I think perhaps "at that date" is widely used in the UK, but I'm not sure. (BE speakers, what is your opinion?) Personally, I always write "on that date", but I accept "at that date" when I read it.

Both phrases are a bit formal. They are used in writing, but I don't think I have ever heard either one in conversation. If I want to express the idea of "at that date" in spoken English, I would say "at the time" or "back then" (for past dates), or "by that time" or "by then" (for future dates).

I would only use "at that date" in a specific situation, and usually the wording would be "as at that date" or "as at 12 May 2005".
E.g. We require your company's balance of accounts as at the date of the merger.
At the date of the merger the company was essentially bankrupt.
There were no funds left in the company accounts at that date.

Otherwise, in every ordinary sense, I would say "on that date", "on 12 May 2005", etc. (the meaning being essentially the same as "on that day")
E.g. She left for New York on the same date as her brother left for London.
Were there any other passengers listed on that date?...on 25 June 2005?
The contract expires on 30 June 2006. On that date your employment will terminate.

Actually using "that date" would be less common than writing the actual date or name of the event itself.

I would also usually use "on that date".

The only exception, where I would use "at that date" would be when recounting something historical, e.g. "Hitler Germany and Stalinist Russia signed a pact of non-aggression on (insert date). However, at that date both sides were already planning the invasion of the other).

Otherwise I agree with Mary


I can't confirm though, that 'at that date' is commonly used in BE