A study of proton-proton collisions in which two $b$-hadrons are produced in association with a $Z$ boson is reported. The collisions were recorded at a centre-of-mass energy of 7 TeV with the CMS detector at the LHC, for an integrated luminosity of 5.2/fb. The $b$-hadrons are identified by means of displaced secondary vertices, without the use of reconstructed jets, permitting the study of $b$-hadron pair production at small angular separation. Differential cross sections are presented as a function of the angular separation of the $b$-hadrons and the $Z$ boson. In addition, inclusive measurements are presented. For both the inclusive and differential studies,different ranges of $Z$ boson momentum are considered.
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