  The Banach $^{*}$-algebra $A\hat{\otimes}B$, the operator space projective
tensor product of $C^{*}$-algebras $A$ and $B$, is shown to be $^{*}$-regular
if Tomiyama's property ($F$) holds for $A\otimes_{\min}B$ and $A
\otimes_{\min}B=A \otimes_{\max}B$, where $\otimes_{\min}$ and $\otimes_{\max}$
are the injective and projective $C^{*}$-cross norm, respectively. However,
$A\hat{\otimes}B$ has a unique $C^{*}$-norm if and only if $A\otimes B$ has. We
also discuss the property ($F$) of $A\hat{\otimes}B$ and $A\otimes_{h}B$, the
Haagerup tensor product of $A$ and $B$.
