  We investigate the intrinsic reason for spin statistics connection. It is
found that if a free field theory is rotationally (SU(2)) invariant, and has
time reversal ($T$) and charge conjugation ($C$) symmetries, it obeys the spin
statistics connection, except for a special case. Shr{\"o}dinger equation
belongs to this special case, and does not obey spin statistics connection.
Further we show that if the energy spectrum of a particle $E(p)$ takes the form
of a square root, namely contains branch points in the complex $p$ plane, the
particle cannot belong to this special case, and must obey the spin statistics
connection. This conclusion includes the relativistic particles as a particular
example.
