The phrase "tenuous connection" means that there is a weak or fragile relationship between two things or ideas. It suggests that there isn't much evidence or support to back up the connection. Full definition
For a while the only tenuous connection between brain and body (mind, higher levels of thought weren't possible without complete breakdown) was furiously playing Triple Town, a phone game where you attempt to build a town around small, evil bears who thwart your progress. (bombmagazine.org)
Radical theology had only tenuous connections with secular theology, which was primarily a reformist species of the classical biblical theology of creation. (religion-online.org)
Wong Kar - wai's Chungking Express (1994) captures the whiplash rhythms and tenuous connections of urban life in a bifurcated story that follows two heartsick Hong Kong cops (Takeshi Kaneshiro and Tony Leung) who cross paths at the Midnight Express take - out restaurant stand, where the ethereal pixie waitress Faye (Faye Wong) works. (criterion.com)