From Gypsy Jazz Guitar Wiki
Half-diminished chords (m7/5b)
There are three basic positions for these chords widely used in various standards.
Root on the lower E string (Am7/5b here) mostly played with the root between F# and C:
Root on the A string (Dm7/5b here) mostly played with the root between Bb and F with the index muting the lower E string:
Root on the A string (Dm7/5b here) mostly used with the root between B and F with the middle finger muting the lower E string: