Is Tachanun said on 3 Tammuz?

The Rebbe was asked this question and responded that if one asks this question, that itself is an indication that the questioner lacks the “hergesh” (feeling).

Practically, this question might be better answered by your personal mashpia.

מענה מט’ תמוז תשמ”ט: ״בענינים התלוים ברגש – אין לשאול כיון שזוהי הוכחה שאין רגש״.