MtheGM, I'm not sure what you mean by "respectable" research.

I don't think the tools exist to come close to objectively measuring or observing the varied but considerable reported anecdotal phenomena that currently get labeled telepathy exist. There is research. The quality of that research, for any number of reasons, is such that none of it can be considered "respectable" from the standpoint of being able to draw any conclusions from it. Some of it may barely pass muster to suggest areas for further study or to suggest ways to tweak the experimental design or the tools to measure and repeat to offer some hope that the next experiment may have slightly more validity, and therefore suggest further refinements.