How was Sherlock Holmes connected to The Curious Incident of the Dog in the Night-Time?

Christopher compares himself to Sherlock Holmes when he is trying to find out who killed the dog. This is because he calls himself a 'detective'.

In the Sherlock Holmes short story 'Silver Blaze' we find the following passage:

Inspector Gregory: "Is there any other point to which you would wish to draw my attention?"

Sherlock Holmes: "To the curious incident of the dog in the night-time."

Inspector Gregory: "The dog did nothing in the night-time."

Sherlock Holmes: "That was the curious incident," remarked Sherlock Holmes.