Another fingering for a c#dim is 3x232x. Dave's turnaround could be fingered: C-3x555x, C#dim-3x323x, Dm7-5x353x, G7-3x343x.
I don't have a guitar in my hands, so I hope that's right. I often make the C-x3555x, but with the first way, I think it's C/G, you use the same combination of strings for all chords.