According to LSJ, the epigraphic evidence is mixed for the perf. act. -- τέθηκα, τέθεικα. An Attic inscription has τέθηκα, but other inscriptions show τέθεικα. LSJ goes on to state that some editors restore τέθηκα in Attic texts, implying that the mss. read τέθεικα. The medio-passive form τέθειμαι isn't used very much. Smyth sec. 767 says that τέθειμαι "even in composition is rare and is unknown on Attic inscriptions." As Nolmendil indicates, keimai is usually used as the perf. passive of τίθημι. Chantraine, Morphologie historique du grec (p. 192) says that the "rare et tardive" form τέθειμαι was formed by analogy with heimai.
We should probably not think of τέθειμαι as the medio-passive of τίθημι, but instead think of τίθημι as defective or suppletive in the perfect medio-passive.