  We provide a construction of local and automorphic non-tempered Arthur
packets of the group SO(3,2) and its inner form SO(4,1) associated with a
certain Arthur's parameter and prove a multiplicity formula.
  We further study the restriction of the representations in these packets to
the subgroup SO(3,1). In particular, we discover that the local Gross-Prasad
conjecture, formulated for generic L-packets, does not generalize naively to a
non-generic A-packet. We also study the non-vanishing of the automorphic
SO(3,1)-period on the group SO(4,1) x SO(3,1) and SO(3,2) x SO(3,1) for the
representations above.
  The main tool is the local and global theta correspondence for unitary
quaternionic similitude dual pairs.
