Can you play a c minor chord in a c major scale?
yes and no:
you might get away with an empty 5th of C and G in the left hand and then using the Eb in the right hand as part of some melodic idea
you could also use it as substitute for F (chord IV) in a progression; akin to the usage found in some country songs and pop ballads
i.e.
I-IV-iv-I-VI-II-V-I ~ C-F-Fm-C-A-D-G-C,
[mp3]http://www.bandcoach.org/fp/audio/cminOnCMaj-01.mp3[/mp3]
switch it up now and substitute the Cm for the F and you get the following
I-i-iv-i-VI-II-V-I ~ C-Cm-Fm-Cm-A-D-G-C,
[mp3]http://www.bandcoach.org/fp/audio/cminOnCMaj-02.mp3[/mp3]
now substitute the C minor in the right hand over the F major in the left hand to get Fdom9 a polychord
I-i/IV-iv-i-VI-II-V-I ~ C-Cm/F-Fm-Cm-A-D-G-C,
[mp3]http://www.bandcoach.org/fp/audio/cminOnCMaj-03.mp3[/mp3]
note the use of secondary dominants in the last four chords: A is the dominant of D is the dominant of G is the dominant of C: Adding C# for the A and F# for the D is considered acceptable practice even though we are in C major
more succinctly context is everything