Let D be a quaternion division algebra over a non-archimedean local field F of characteristic zero. Let E/F be a quadratic extension and SL∗n(E)=GLn(E)∩SLn(D). We study distinguished representations of SLn(D) by the subgroup SL∗n(E). Let π be an irreducible admissible representation of SLn(D) which is distinguished by SL∗n(E). We give a multiplicity formula, i.e. a formula for the dimension of the C-vector space HomSL∗n(E)(π,\mathbbm1), where \mathbbm1 denotes the trivial representation of SL∗n(E). This work is a non-split inner form analog of a work by Anandavardhanan-Prasad which gives a multiplicity formula for SLn(F)-distinguished irreducible admissible representation of SLn(E).