Probabilistic record linkage techniques assign match weights to one or more potential matches for those individual records that cannot be assigned 'unequivocal matches' across data files. Existing methods select the single record having the maximum weight provided that this weight is higher than an assigned threshold. We argue that this procedure, which ignores all information from matches with lower weights and for some individuals assigns no match, is inefficient and may also lead to biases in subsequent analysis of the linked data. We propose that a multiple imputation framework be utilised for data that belong to records that cannot be matched unequivocally. In this way, the information from all potential matches is transferred through to the analysis stage. This procedure allows for the propagation of matching uncertainty through a full modelling process that preserves the data structure. For purposes of statistical modelling, results from a simulation example suggest that a full probabilistic record linkage is unnecessary and that standard multiple imputation will provide unbiased and efficient parameter estimates.