A signed total double Roman dominating function (STDRDF) on an isolated-free graph G = ( V , E ) is a function f : V ( G ) → { − 1 , 1 , 2 , 3 } such that (i) every vertex v with f ( v ) = − 1 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 f ( w ) ≥ 2 and (iii) ∑ u ∈ N ( v ) f ( u ) ≥ 1 holds for any vertex v. The weight of a STDRDF is the value f ( V ( G ) ) = ∑ u ∈ V ( G ) f ( u ) . The signed total double Roman domination number γ sdR t ( G ) is the minimum weight of a STDRDF on G. In this article, we provide various bounds on γ sdR t ( G ) 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.