I know I replied to your post in the other thread, but just to be complete... The ".cpi" file does not contain any actual video or audio data, but it does have information *about* the video and audio contained in the MTS files
http://www.fileinfo.com/extension/cpi
The .cpi file contains only indexed text information that the camcorder uses for playback or if the camcorder's built-in effects are used for playback from the camcorder.

If the video (and .cpi) files are still in the camcorder, then connect the camcorder and Mac, and do the import/capture as you previously (successfully) had done. If the MTS files have been copied from the camcorder to the Mac (along with the .cpi file), then the MTS files will need to be converted to a file format iMovie can deal with (MOV or MP4 are most common). To do this conversion - transcoding - a utility applications is required.

Download and install MPEG StreamClip
http://www.apple.com/downloads/macosx/video/mpegstreamclip.html
Transcode the MTS files. Launch iMovie, drag the converted files to iMovie's sequence area... In this transcoding case, the .cpi files are useless.

There are other transcoders - I happen to like MPEG StreamClip. HandBrake http://handbrake.fr/ is another very useful video editing tool... Audacity http://audacity.sourceforge.net/ is a very useful and powerful audio editor.