In vacuum the molecule has three possible Lewis structures (valence bond structures). One is shown above. The others involve the positive charge on one of the two other nitrogen atoms. The molecule should have D_3h symmetry and the ground state should be non-degenerate and the first excited state two-fold degenerate.
However, in 1942 G.N. Lewis pointed out that the optical absorption spectrum showed a shoulder and suggested that at room temperature two structural isomers may be accessible.
A fascinating article, Crystal violet’s shoulder by Scott Lovell, Brian J. Marquardt and Bart Kahr, reviews how the question of whether the shoulder arose from two "ground" states or two close excited states was still not resolved in 1999.
The main possible source of symmetry breaking would be the local environment (solvent, counter-ions, neigbouring CV molecules, ...).
The excited state symmetry could be reduced by a Jahn-Teller effect.
As an aside I give two fascinating quotes from the article:
as the active ingredient in carbon paper it [Crystal Violet] has stained more hands than any other compound...
The determination of the X-ray structure of CV+Cl- was first attempted in 1943 by Krebs, a wartime worker at the I.G. Farben Oppau explosives factory which was eventually bombed by the Allied Forces. On 25 March 1945, British and American investigators organized bands of local Germans to dig through the factory rubble in order to retrieve scientific documents that might aid the Allies in the defeat of Japan. During this search they unearthed a report by Krebs describing his preliminary crystallographic studies, dated 15 June 1943. It was cataloged with the reports of the British Intelligence Objectives Sub-committee (BIOS),one of several special scientific intelligence units formed to collect technical information of military value from the Germans. BIOS microfilms can be obtained from the US Library of Congress.A 2010 JACS paper claims to finally show that the origin of the shoulder is due to two excited states whose degeneracy is lifted by the solvent.
First Hyperpolarizability Dispersion of the Octupolar Molecule Crystal Violet: Multiple Resonances and Vibrational and Solvation Effects
Jochen Campo, Anna Painelli, Francesca Terenziani, Tanguy Van Regemorter, David Beljonne, Etienne Goovaerts and Wim Wenseleers
A key aspect of the article is using an effective Hamiltonian acting on the relevant valence bond structures...
but more on that later...