David,
Certain mental illnesses do run in families. However, a specific genetic defect that is reproducible over time and through out society has not been found for any mental illness.
Family-linkage and twin studies have indicated that genetic factors often play an important role in the development of mental disorders. The reliable identification of specific genetic susceptibility to particular disorders, through linkage or association studies, has proven very difficult, if not impossible.
The heritability of behavioral traits associated with mental disorder may be greater in permissive than in restrictive environments (families). This has been reported to be likely due to the complexity of interactions between genes, environmental events, and early development.
And susceptibility genes probably work through both "within-the-skin" (physiological) pathways and "outside-the-skin" (behavioral and social) pathways. Investigations increasingly focus on links between genes and specific traits (including neurophysiological, biochemical, endocrinological, neuroanatomical, cognitive, or neuropsychological)—rather than disease categories.
With regard to a prominent mental disorder, Schizophrenia, for a long time consensus among scientists was that certain alleles (forms of genes) were responsible for schizophrenia, but some research has indicated only multiple, rare mutations, thought to alter neurodevelopmental pathways that can ultimately contribute to schizophrenia; virtually every rare structural mutation was different in each individual. Therefore, there was no real gene defect to account for the disorder.
So, yes, some mental illnesses do run in families. But, there is no identifiable genetic defect that can be seen on the genes for any specific mental illness. You cannot do a gene study, actually physically looking at the genes, and be able to say that this person has a mental illness. The genetic study would have to be a family study, looking at the family memeber's past medical histories.
Good luck.