It's not mentioned anywhere that Scar killed his father. But it would make sense of all-benevolent Mufasa's lack of empathy towards his brother.
And if I may draw more mythology into this, why Scar hates the song "It's a small world" is because Ahadi used to sing it to them when they were cubs, and it reminds of him of his treachery. I'd like to hear from you guys some more theories, against or pro.
UPDATE: A lot of 'against' theories are based on the fact that Mufasa would banish Scar from the Pride, had he seen his brother's act. Very agreeable. He wouldn't want a killer loose among his loved ones. But still, according to the canon, Mufasa forgave Scar when he tried to set a buffalo on him (which went wrong and gave taka the scar in return). Could it be that Scar pleaded with Mufasa and he forgave him? or maybe even Mufasa didn't really see Scar pushing Ahadi off the cliff, but just got there in time to see Scar standing there... putting on an act as he tried to save their father, but he lost the grip?
======What we learned======
Mufasa doesn't know Scar pushed him over. He looked like he was helping him. But something at the back of his mind nabs at Mufasa. Scar's story doesn't add up. He would keep an eye on his brother from then on.