We constrain the total Higgs boson width, , using off-shell production and decay to four leptons, , or two leptons plus two neutrinos, , with . The analysis is based on the data collected in 2012 by the CMS experiment at the LHC, corresponding to an integrated luminosity at a center-of-mass energy \surd s = 8 \, {\rm TeV}. The analysis uses the ZZ invariant mass distribution as well as a matrix element likelihood discriminant to separate the ZZ components originating from gluon- and quark-initiated processes. The analysis relies on the transverse mass or missing transverse energy distributions in jet categories. An unbinned maximum-likelihood fit of the above distributions, combined with the measurement near the resonance peak, leads to an upper limit on the Higgs boson width of at the 95\% confidence level, assuming \Gamma_{\mathrm{H}}^{\mathrm{SM}} = 4.15 \, {\rm MeV}. This result considerably improves over previous experimental constraints from the measurement near the resonance peak.