Whether it's masking tape used while painting walls and trim or duct tape, sometimes you're left with a sticky residue remaining. I've had several experiences with this, on painted wood, and you don't want to use a solvent.
Pour a small amount of vegetable, corn or olive oil into a bowl, using a wad of paper towels, blot the tape residue with oil. You want it well coated, but not dripping. Let it sit for 60 minutes. Wipe the wood with a clean white cloth to remove the residue and oil. If any residue remains, apply more oil and let it sit for 30 minutes more. Wipe with a clean white cloth, rubbing additional oil until no adhesive residue remains. Add a few squirts of grease-fighting dish detergent, I use regular, Dawn into a small basin of warm water. Dip a sponge or soft rag in the soapy water and wipe the olive oil residue off the surface. Rinse, then dry the painted wood surface with clean, soft cloth.