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In the present work, we report calculations of resonances in the positron-hydrogen system interacting with screened Coulomb potentials using the method of complex scaling together with employing correlated Hylleraas wave functions. Resonances with natural and unnatural parities are investigated. For the natural parity case, resonance parameters (energy and width) for D-wave resonance states with even parity lying below various positronium and hydrogen thresholds up to the H(N = 4) level are determined. For the unnatural parity case, results for P-even and D-odd resonance states with various screened Coulomb interaction strengths are located below different lower-lying Ps and H thresholds.