David Gail's sudden death is under investigation ... and cops tell us they are looking into the possibility of a fatal drug overdose.

Law enforcement tells TMZ ... no foul play is suspected in David's case but police are waiting for toxicology tests to determine an official cause of death. With that said, we're told an OD is what police suspect might've gone down here. No word on what type of substances are on cops' radar just yet.

As we reported ... David's sister, Katie Colmenares, announced his death Saturday in a social media post -- leaving a sweet and touching remembrance in confirming his passing.

His sibling did not give a cause of death for her brother -- but did say she would "hold you so tight every day in my heart." She also said she'll miss David "every second of every day forever."

Remember ... David famously appeared in 7 episodes of 'BH: 90210' as Stuart Carson, the fiancé of Shannen Doherty's character. DG was also big in the soap opera world ... he's in 216 episodes of the "General Hospital" spin-off "Port Charles."

His other acting credits include ... "Matlock," "Murder, She Wrote," "The Round Table," "Doogie Howser, M.D.," "Perfect Opposites" and "Growing Pains." On the big screen, David starred alongside Bradley Cooper in the 2002 rom-com "Bending All The Rules."

David was only 58.