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In this paper, we prove the strong unique continuation property at the originfor solutions of the following scaling critical parabolic differentialinequality  \[  |\operatorname{div} (A(x,t) \nabla u) - u_t| \leq \frac{M}{|x|^{2}} |u|,\ \ \\  \]  where the coefficient matrix $A$ is Lipschitz continuous in $x$ and $t$. Ourmain result sharpens a previous one of Vessella concerned with the subcriticalcase as well as extends a recent result of one of us with Garofalo and Mannafor the heat operator.

Strong unique continuation for variable coefficient parabolic operators with Hardy type potential