Given a random sample of observations, mixtures of normal densities are often
used to estimate the unknown continuous distribution from which the data come.
Here we propose the use of this semiparametric framework for testing symmetry
about an unknown value. More precisely, we show how the null hypothesis of
symmetry may be formulated in terms of normal mixture model, with weights about
the centre of symmetry constrained to be equal one another. The resulting model
is nested in a more general unconstrained one, with same number of mixture
components and free weights.