The near-Earth asteroid (196256) 2003 EH1 has been suggested to have a dynamical association with the Quadrantid meteoroid stream. We present photometric observations taken to investigate the physical character of this body and to explore its possible relation to the stream. We find no evidence for on-going mass-loss. A model fitted to the point-like surface brightness profile at 2.1 AU limits the fractional contribution to the integrated brightness by near-nucleus coma to $leq$ 2.5 %. Assuming an albedo equal to those typical of cometary nuclei ($it p_{rm R}$=0.04), we find that the effective nucleus radius is $r_e$ = 2.0$pm$0.2 km. Time-resolved ${it R}$-band photometry can be fitted by a two-peaked lightcurve having a rotational period of 12.650$pm$0.033 hr. The range of the lightcurve, $Delta m_{rm R}$= 0.44 $pm$ 0 .01 mag, is indicative of an elongated shape having an axis ratio $sim$1.5 projected into the plane of the sky. The asteroid shows colors slightly redder than the Sun, being comparable with those of C-type asteroids. The limit to the mass loss rate set by the absence of resolved coma is $lesssim$ 2.5$times$ 10$^{-2}$ kg ${rm s^{-1}}$, corresponding to an upper limit on the fraction of the surface that could be sublimating water ice $f_A$ $lesssim$ 10$^{-4}$. Even if sustained over the 200-500 yr dynamical age of the Quadrantid stream, the total mass loss from 2003 EH1 would be too small to supply the reported stream mass ($10^{13}$ kg), implying either that the stream has another parent or that mass loss from 2003 EH1 is episodic.
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