We introduce the notion of t-approximated determinisation and the t-twinning property of weighted tree automata (WTA) over the tropical semiring. We provide an algorithm that accomplishes t-approximated determinisation of an input automaton A, whenever it terminates. Moreover, we prove that the t-twinning property of A is a sufficient condition for the termination of our algorithm. Ultimately, we show decidability of the t-twinning property for WTA.