We present new near-infrared (1.1-micron) observations of the circumstellar environment of the planet-bearing star 55 Cancri. With these Hubble Space Telescope images we are unable to confirm the observation of bright scattered radiation at longer NIR wavelengths previously reported by Trilling & Brown (1998), and Trilling, Brown & Rivkin (2000). NICMOS coronagraphic images with detection sensitivities to ~ 100 microJy arcsec$^{-2}$ at 1.1 microns in the region 28 - 60 AU from the star fail to reveal any significant excess flux in point- spread-function (PSF) subtracted images taken in two Hubble Space Telescope orbits. These new observations place flux densities in the 19-28 AU zone at a factor of ten or more below the reported ground-based observations. Applying a suite of a dozen well-matched coronagraphic reference PSFs, including one obtained in the same orbits as the observations of 55 Cnc, yielded consistently null results in detecting a disk. We also searched for, and failed to find, a suggested flux-excess anisotropy in the ratio of ~1.7:1 in the circumstellar background along and orthogonal to the plane of the putative disk. We suggest that, if such a disk does exist, then the total 1.1-micron spectral flux density in an annular zone 28 - 42 AU from the star must be no more than ~0.4mJy, at least ten times smaller than suggested by Trilling and Brown, upon which their very large estimate for the total dust mass (0.4~$M_{\earth}$) was based. Based on the far infrared and submillimeter flux of this system and observations of scattered light and thermal emission from other debris disks, we also expect the intensity of the scattered light to be at least an order of magnitude below our upper limits. Comment: 40 pages, accepted to AJ 03OCT2000; 7 figures available at: http://nicmosis.as.arizona.edu:8000/PREPRINTS/55CNC/55_CNC_PREPRINT.html