In the complex, ${\mathrm{BH}}_3\mathrm{CO}$, what is the type of back bond from B to C ?

The type of Bh3Co back bond from B to C is $\sigma \to {\pi }^{\ast }$.

Structure of this molecule is,

When one atom in a compound has a single electron and the other has an open orbital adjacent to it, back bonding, a type of bonding, happens between the two atoms. A molecule with back bonding possesses pi-bonding properties because pi-bonding happens after the sigma bond forms.