A Nordhaus-Gaddum-type result is a (tight) lower or upper bound on the sum or product of a parameter of a graph and its complement. In this paper we study Nordhaus-Gaddum-type results for total domination. We examine the sum and product of γ_t(G₁) and γ_t(G₂) where G₁ ⊕G₂ = K(s,s), and γ_t is the total domination number. We show that the maximum value of the sum of the total domination numbers of G₁ and G₂ is 2s+4, with equality if and only if G₁ = sK₂ or G₂ = sK₂, while the maximum value of the product of the total domination numbers of G₁ and G₂ is max{8s,⌊(s+6)²/4 ⌋}.