A signed total double Roman dominating function (STDRDF) on an isolated-free graph [Formula: see text] is a function [Formula: see text] such that (i) every vertex v with [Formula: see text] has at least two neighbors assigned 2 under f or one neighbor w with f(w) = 3, (ii) every vertex v with f(v) = 1 has at least one neighbor w with [Formula: see text] and (iii) [Formula: see text] holds for any vertex v. The weight of a STDRDF is the value [Formula: see text] The signed total double Roman domination number [Formula: see text] is the minimum weight of a STDRDF on G. In this article, we provide various bounds on [Formula: see text] and we show that the corresponding decision problem is NP-complete for bipartite and chordal graphs. In addition, we determine the signed total double Roman domination number of some classes of graphs including cycles, complete graphs and complete bipartite graphs.