In either case, India wouldn't need evidence from anybody else to determine its own innocence or guilt, because surely it knows whether it did what it is being accused of doing.
Even if this murder thing is true, it could have been some rogue agent in the government. In that case the evidence would flush them out. India does have a lot to lose, reputationally, in this case. But not enough to lose that they would simply accept whatever Canada says.
From the Indian point of view Canada has also brushed off situations where India approached them with evidence against Canadian citizens. So if Canada now approaches with demands of their own, dismissing these is perfectly alright without precise evidence.
India has no obligation to preserve whatever sources some 5 eye(I) country has within their government, and just cooperate with Canada no questions asked.
From my perspective, the crime would need to be officially sanctioned by the person or people in power, for it to be called "done by the government". Just like if a US government employee is turned rogue, deciding to act against the US government, I wouldn't say that the US government is now against the US government.