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We investigate the intrinsic reason for spin statistics connection. It isfound that if a free field theory is rotationally (SU(2)) invariant, and hastime reversal ($T$) and charge conjugation ($C$) symmetries, it obeys the spinstatistics connection, except for a special case. Shr{\"o}dinger equationbelongs 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 formof a square root, namely contains branch points in the complex $p$ plane, theparticle cannot belong to this special case, and must obey the spin statisticsconnection. This conclusion includes the relativistic particles as a particularexample.

The Cornerstone Of Spin Statistics Connection: The SU(2)$\times$ C $\times$ T Symmetry