A study of the sensitivity for the inclusive production of Standard Model Higgs bosons ${\rm H}$ decaying in ZZ$^{(*)}$ pairs is presented with the CMS experiment at the CERN LHC $pp$ collider at 14 TeV centre of mass energy, for the integrated luminosity of 1 fb$^{-1}$. The analysis is performed for the leptonic decay channels ${\rm H} \rightarrow {\rm Z}{\rm Z}^{(*)} \rightarrow 4\ell$ with $\ell = e, \mu$ and for a mass $m_{\rm H}$ in the range from $120$ to 250 \GeVcc. Signal and background datasets obtained with a detailed Monte Carlo simulation of the detector response, including the limited inter-calibration and alignment precision expected at startup luminosities, are treated using a complete reconstruction chain. A simple $m_{\rm H}$ independent sequence of cuts is established which provides a clean sample of $4\ell$ events while preserving the highest signal detection efficiency. A signal with a significance above 2 standard deviations is found unlikely for a Higgs boson with a mass $m_{\rm H}$ lying anywhere in the mass range considered. In absence of significant deviations from background expectations, upper limits on the production cross-section of a Standard Model-like Higgs boson can be established. The limits extend beyond existing constraints.

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