We carried out a survey of (CO)-C-13 cloud cores in the Ophiuchus region (l = 355-degrees-12-degrees; b = 15-degrees-23-degrees) in the north of the rho Oph molecular cloud core by using results of a (CO)-C-12 unbiased survey as a guide. Observations of the J = 1-0 (CO)-C-13 emission were made with the 4 m millimeter telescope at Nagoya University (HPBW = 2'.7), and 7909 (CO)-C-13 spectra were obtained at a spacing of 2' or 4'. The overall (CO)-C-13 distribution is highly clumpy and filamentary. The (CO)-C-13 distribution is separated into 23 regions as traced by a 3-sigma contour level, including more than 50 pronounced localized maxima. On the basis of these data we identified 23 (CO)-C-13 clouds and 51 (CO)-C-13 cores. The total mass of the (CO)-C-13 clouds is estimated to be (4 +/- 2) X 10(3) M., and the typical densities of the (CO)-C-13 cores are around 3 X 10(3) cm-3. Lists of physical parameters such as size, mass, average density, etc., are presented for all the (CO)-C-13 clouds and cores. The mass spectrum of the (CO)-C-13 cores is well fitted by a power law with an index value of approximately 1.7, similar to those published so far for the other cloud cores. Dynamical stability of the (CO)-C-13 cores is tested by using the virial theorem. The result indicates that the necessary conditions for dynamical equilibrium are nearly satisfied by most of the (CO)-C-13 cores. The (CO)-C-13 clouds do not exhibit a sign of active star formation; that is, only about 10 young stellar objects are associated with the (CO)-C-13 clouds as a whole. There are 13 promising candidates for young stellar objects formed in the cloud complex. They are 11 IRAS point sources including four T Tauri-type stars, and two T Tauri-type stars not detected by the IRAS. Four of the IRAS point sources seem to be protostellar according to their far-infrared colors. The luminosities of the IRAS point sources are less than 4 L., and most of them range from 0.2 L. to 1.6 L.. Spectral types of the six T Tauri-type stars are later than G5. These facts suggest that only low-mass stars are formed in the Ophiuchus north region except for one (CO)-C-13 cloud where external triggering may have played a role, resulting in formation of a few early-type stars. By comparing the molecular mass with the young stellar mass, we have obtained a conservative estimate for the upper limit of the star formation efficiency to be approximately 0.3% in the Ophiuchus north region. This efficiency is significantly lower than that of the rho Oph main core, greater-than-or-equal-to 20%, and those in the Galaxy, several percent, too. We discuss a possibility that such a low star formation efficiency has been caused by a high degree of ionization of the (CO)-C-13 cores in the Ophiuchus north region due to the higher far-ultraviolet flux from nearby Scorpius OB2 association.