When referring to a past date would you say: On 'this' date, something happened or On 'that' date, something happened?

Example: Jessica was seen on May 3, 2013. On this date, or On that date, she reported seeing a cat in the tree.

Thank you!

Both are possible. "That" is a little clearer as "this" could mean today.

(If you're interested, they are called demonstrative adjectives.)

Thank you! Exactly what I thought. This to me means today, in the present.