Here's (more or less) what was said in the Burke episode. I'm not the best transcriptionist and I took it off the television - no DVD.
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Before any Chan reference, Burke speaks a possible “Chan-ism” with pidgin English
Burke: wise man hide leaf in forest
A little later:
Burke: Killer always returns to the scene of the crime.
Tim: Did they teach you that at the Police academy?
Burke: No, I learned that from old Charlie Chan movies.
Later still:
Tim: Who do you think did it, Captain?
Burke: Nev’r ask a quextion in “Charlie chan movie. (in bad pidgin English)
Later still:
Les: (referring to suspects) 3 down and one to go.
Burke: It better be one or my theory and Charlie Chan go out the window
And finally:
Les: Charlie Chan couldn’t have done it better.
Burke: (to Les with slight bow) Thank you number one son.