The main interest of the cytogenetic dosimetry is the prevision of an unknown radiation dosage based in cytogenetic analysis. In this paper the dosimetry problem is formulated as a linear calibration problem for binary response data. Two approaches are considered for inference on the quantity of interest, which is expressed as a calibration parameter in a discrete response variable situation. One is based on the maximum likelihood approach, which depends on large sample results and the second one is based on a Markov chain Monte Carlo (MCMC) simulation approach using BUGS. Application to a data set obtained from blood cultures exposed in vitro to Cobalt 60 (.60Co) at the Energetic Nuclear Research Center (IPEN-Brasil) is considered.