The first dedicated search for the η c2 (1D) is carried out using the decays B + → η c2 (1D)K + , B 0 → η c2 (1D)K 0 S , B 0 → η c2 (1D)π − K + , and B + → η c2 (1D)π + K 0 S with η c2 (1D) → h c γ. No significant signal is found. For the η c2 (1D) mass range between 3795 and 3845 MeV/c 2 , the branching-fraction upper limits are determined to be B(B + → η c2 (1D)K +) × B(η c2 (1D) → h c γ) < 3.7 × 10 −5 , B(B 0 → η c2 (1D)K 0 S) × B(η c2 (1D) → h c γ) < 3.5×10 −5 , B(B 0 → η c2 (1D)π − K +)×B(η c2 (1D) → h c γ) < 1.0×10 −4 , and B(B + → η c2 (1D)π + K 0 S) × B(η c2 (1D) → h c γ) < 1.1 × 10 −4 at 90% C.L. The analysis is based on the 711 fb −1 data sample collected on the Υ(4S) resonance by the Belle detector, which operated at the KEKB asymmetric-energy e + e − collider.