<p>Reference intervals are often considered the most widely used medical decision-making tool. These intervals are vital and key to the well-grounded interpretation of results in laboratory medicine. For complicated types of diagnoses, such as the assessment of kidney function, it is necessary to look into multiple analytes. The use of separate reference intervals which fail to consider the correlations among the analytes is inappropriate. Instead, the multi-dimensional nature of the problem requires a multivariate reference region (MRR). This study develops sound statistical methodologies to compute MRRs that account for the cross-correlations among analytes. While MRRs have been available in the laboratory medicine literature, these MRRs are mostly of ellipsoidal shape, especially when constructed under multivariate normality. One weakness of ellipsoidal reference regions is its inability to detect if a specific analyte is within its normal range. To address this problem, this study develops rectangular MRRs, since such regions are easily interpretable and can detect component-wise outlying measurements. The criterion used to compute the MRRs is that of a rectangular tolerance region. We develop the methodologies under a nonparametric setting, since almost all laboratory test results are not normally distributed. The proposed methodologies yield accurate results, with coverage probabilities close to the nominal level.</p>