Make a copy of both letters.
Those need to be outlined. Then apply the stroke to the copy.
Outline the stroke.
Cut the stroked letters in half (e.g. with the eraser tool) and keep the lower half of the C and the upper half of the T.
Then use the parts for punching the letters (pathfinder panel).
Go into outline view and delete what you don't need.
With what you have (both letters outlined), you can:
1) Select the T and in the Appearance palette flyout tick Add New Stroke, then select it in the main window and drag it down beneath the Fill, change it to white, then in the Stroke palette increase the Stroke Weight;
2) Repeat 1) for the C;
This should give the white parts to cover the other letter at the crossings;
3) With the Line Tool drag across the C to the left and Object>Path>Divide Object Below to split the C in two, see 5 for the white part across;
4) Select the upper part of the C in the Layers palette and drag it down beneath the T;
5) Click the top segment of the lower part of the C with the Direct Selection Tool and press Delete once to get rid of the white part across.