The molecular design rules of organic nonlinear optical (NLO) materials are well established, especially those pertaining to the first-order molecular hyperpolarizability, beta, which governs second harmonic generation (SHG): a phenomenon that is responsible for the frequency doubling processes in many optical applications. The availability of these rational guidelines has propelled the development of new organic SHG chromophores. Conversely, the development of organometallic SHG-active complexes has not been steered so clearly. Many reports on individual series of complexes suggest a singular correlation between their structure and SHG properties. Several reviews have catalogued such results, but these have only distinguished compounds by chemical type, while their SHG properties are described one-by-one for each chemical. We herein propose a generic classification scheme that can systematically rationalize dipolar SHG properties for all organometallic complexes. This classification method stands to provide the holistic information that is needed to generate a rational set of guidelines for the systematic molecular design of dipolar SHG-active organometallic chromophores. Our scheme shows that only a simple set of molecular design rules is required to relate the chemical structure of an organometallic complex to its second-order dipolar SHG properties. This is despite the fact that these molecular design rules are rooted in a complicated panoply of ligand- and crystal-field theory, resonance structures, intramolecular charge transfer considerations, metal oxidation states, and metal coordination attributes. While the roots of these rules can be derived at the individual chemical level, their derivation via our workflow of simple decision-making processes which connect these rules within a simple classification scheme, stands to facilitate a rational molecular design approach toward the materials discovery of organometallic complexes for SHG applications.