Question Depression Screenings

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Hello , I need clarification on which CPT codes should I use for depression screenings for Medicare and Commercial Payers.
I know that we should use G0444 for Medicare patients along with G0439 or it will be applied to patient copay or deductible.
Should G0444 be used for all payers? My understanding is that G0444 is used for Medicare patients only. Our office use the PHQ 9 form for all patients who are being seen for wellness visits.

Example: Patient has IMA insurance (commercial)
99396 balance was paid in full
G0444 balance was applied to patient deductible.
Patient is 59 years of age .

Should I have use 96127?