Products formed when solid CuCN is dissolved in aqueous KCN solution Copper cyanide forms a complex coordination compound, when dissolved in a solution containing excess ($\ce{CN^-}$) ions. 

My question is whether it forms $\ce{[Cu(CN)_4]^{3-}}$ only or both $\ce{[Cu(CN)_3]^{2-}}$ and $\ce{[Cu(CN)_4]^{3-}}$ complexes?

Wikipedia says that both complexes are formed, but I am not sure if its a reliable source.
No, both $\ce{[Cu(CN)3]^2-}$  and $\ce{[Cu(CN)4]^3-}$ species are formed. According to Wikipedia article of copper cyanide:


  ... but rapidly dissolves in solutions containing $\ce{CN−}$ to form
  $\ce{[Cu(CN)3]^2-}$ and $\ce{[Cu(CN)4]^3-}$, which exhibit trigonal
  planar and tetrahedral coordination geometry, respectively. These
  complexes contrast with those of silver and gold cyanides, which form
  $\ce{[M(CN)2]−}$ ions in solution.The coordination polymer
  $\ce{KCu(CN)2}$ contains $\ce{[Cu(CN)2]−}$ units, which link together
  forming helical anionic chains.


See this paper for more details.