A measurement of vector boson ($V$) production in conjunction with a $D^{*}(2010)^+$ meson is presented. Using a data sample corresponding to $9.7, {rm fb}^{-1}$ of ^Mproton-antiproton collisions at center-of-mass energy $sqrt{s}=1.96rm~ TeV$ produced by the Fermilab Tevatron, we reconstruct $V+D^{*+}$ samples with the CDF~II detector. The $D^{*+}$ is fully reconstructed in the $D^{*}(2010)^+ rightarrow D^{0}(to K^-pi^+)pi^+$ decay mode. This technique is sensitive to the associated production of vector boson plus charm or bottom mesons. We measure the ratio of production cross sections $sigma(W+D^{*})/sigma(W)$ = $[1.75pm 0.13 {rm (stat)}pm 0.09 {rm (syst)}]% $ and $sigma(Z+D^{*})/sigma(Z)$ = $[1.5pm 0.4 {rm (stat)} pm 0.2 {rm (syst)}]% $ and perform a differential measurement of $dsigma(W+D^{*})/dp_T(D^{*})$. Event properties are utilized to determine the fraction of $V+D^{*}(2010)^+$ events originating from different production processes. The results are in agreement with the predictions obtained with the {sc pythia} program, limiting possible contribution from non-standard-model physics processes.
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