Hi. I did a quick research on what you'd like to know. When I searched for LogMeIn CTI compatibility, it directed me towards Tenfold's website. Apparently, it's a CTI tool that links different customer databases into a single unified dashboard.
I'm not sure if they can both be integrated, but I think LogMeIn is using Tenfold for their business. I could show you a screenshot but I can't attach an image to my post. You can go here and take a look instead.