A search for CP violation in the phase-space structures of DO and 15° decays to the final states K- K+n-n+ and n-n+n+n- is presented. The search is carried out with a data set corresponding to an integrated luminosity of 1.0fb-1 collected in 2011 by the LHCb experiment in pp collisions at a centre-of-mass ellergy of 7 TeV. For the K-1(+n-n+ final state, the four-body phase space is divided into 32 bins, each bin with approximately 1800 decays. The p-value under the hypothesis of no CP violation is 9.1%, and in no bin is a CP asymmetry greater than 6.5% observed. The phase space of the n-n+n+n- final state is partitioned into 128 bins, each bin with approximately 2500 decays. The p-value under the hypothesis of no CP violation is 41 %, and in no bin is a CP asymmetry greater than 5.5% observed. A complementary search for CP violation is conducted by measuring the difference between P-odd triple product asymmetries for DO and 15° decays to the final state K-1(+n- n+. The measurement is carried out with 2.8 x 105 DO ~ 1(- K+n-n+ candidates from 3 fb- 1 of pp collisions collected by the LHCb experiment during 2011 and 2012. The difference in P-odd triple products asymmetries, AT, is measured to be consistent with zero, AT =( - 0.19 ± 0.20(stat) ± 0.04(sys) ± 0.31(eff))%, where the first component of the uncertainty is the statistical uncertainty, the second component is the combination of the systematical uncertainty, and the third component is the uncertainty associated with the efficiency evaluation, which should decrease significantly with a larger Monte Carlo sample. AT is also measured in 16 bins of the four-body phase space, where each bin has approximately 18,000 DO ~ K- K+n-n+ candidates. The p-value under the hypothesis of no CP violation is 3.2% and no single bin has a value of AT greater than 2.0%. All results are consistent with the hypothesis of no CP violation at the current sensitivity.