Charge on CN- ionWatch
You can go through the accountancy of ascribing a formal charge to both atoms after having drawn Lewis structures, but this is just one approach to deciding which model you wish to use.
The actual structure is a two-centred particle with an overall negative charge.
If you draw out the most popular Lewis structure you end up with a triple bond between the atoms and a lone pair on each atom. The carbon has a formal charge of 1- while the nitrogen has a formal charge of 0.
However, this flies in the face of the higher electronegativity value of nitrogen, which would be expected to be more stable than carbon holding a negative charge.
So the two accountancy theories conflict one another.
For the purposes of A' level the former model, based on Lewis structures and Formal charge is usually considered to be the "answer".
This fits with some empirical evidence, which shows the cyanide ion to coordinate to transition metals via the carbon lone pair, however there are also isonitriles which bond through the nitrogen. So, even empirical evidence is a little ambiguous.