Selection in one sex can produce a correlated response in the other when there is pleiotropy (or linkage disequilibrium) (see Lynch & Walsh 1998, and Lande 1979 & 1980).
Genes can be considered pleiotropic when they affect more than one trait, for example; the male and female forms of equivalent traits, and this can be seen as covariance between the sexes. Cross-sex covariance is common (see Bonduriansky & Rowe 2005, Poissant et al. 2010, Lewis et al. 2011, Griffin et al. 2013, and Blows et al. 2015 for good examples). This means that selection in one sex will often lead to a response in the other.
The correlated response to selection is captured within Lande's multivariate breeders equation, where the change in a vector of traits ($\Delta \bar{z}$) is a result of the genetic variance-covariance matrix ("G-matrix", $G$) multiplied by a vector of selection on the traits ($\beta$).
$\Delta \bar{z} = G \times \beta$
If covariance is zero (i.e. genes have independent male and female effects) then selection does not produce a correlated response in the unselected sex. However, cross-sex covariance is generally present, so correlated responses to selection should impose constraint on the evolution of sexual dimorphism under sexually antagonistic selection. Note that the within-trait cross-sex covariance is in the diagonal elements of the B-submatrix.
One good example of selection on one sex producing a response in the other is this paper. The authors selected on male mandible size in replicate populations of broad horned flour beetles. The mandible is a male limited secondary sexual trait, but selection on the mandible in males produced changes in female fitness and female traits. Selection for larger (smaller) male mandibles resulted in significantly decreased (increased) female abdomen size, and reduced lifetime reproductive success.
"We find that females from populations selected for larger male
mandibles have lower fitness, whereas females in small-mandible
populations have highest fitness, even though females never develop
exaggerated mandibles."
One thing that is really quite cool about that experiment is that the response came in a non-equivalent trait, i.e. it was not female mandibles but other traits that evolved. There is generally less prior probability that there will be a cross-sex cross-trait covariance unless the traits have clear links.
