A search for the lepton-flavour violating decay s2.0-S0370269316000411&_mathId=si1.gif&_user=111111111&_pii=S0370269316000411&_rdoc=1&_issn=03702693&md5=fc1877ec9ab7d383146f53623195cc45" title="Click to view the MathML source">D0→e±μ∓ is made with a dataset corresponding to an integrated luminosity of s2.0-S0370269316000411&_mathId=si2.gif&_user=111111111&_pii=S0370269316000411&_rdoc=1&_issn=03702693&md5=aeceaccfdc386158ce9873498f288901">s2.0-S0370269316000411-si2.gif"> of proton–proton collisions at centre-of-mass energies of s2.0-S0370269316000411&_mathId=si24.gif&_user=111111111&_pii=S0370269316000411&_rdoc=1&_issn=03702693&md5=0aeed9fced1f917d344752e5675b6909">s2.0-S0370269316000411-si24.gif"> and s2.0-S0370269316000411&_mathId=si26.gif&_user=111111111&_pii=S0370269316000411&_rdoc=1&_issn=03702693&md5=e9c1ace21c4d45fb036fe0c92757049a">s2.0-S0370269316000411-si26.gif">, collected by the LHCb experiment. Candidate s2.0-S0370269316000411&_mathId=si5.gif&_user=111111111&_pii=S0370269316000411&_rdoc=1&_issn=03702693&md5=f0e2cdc444fe36fa3f696d6a2040a4a6" title="Click to view the MathML source">D0 mesons are selected using the decay s2.0-S0370269316000411&_mathId=si27.gif&_user=111111111&_pii=S0370269316000411&_rdoc=1&_issn=03702693&md5=35be6e726715a8b901212af5c88ce833" title="Click to view the MathML source">D⁎+→D0π+ and the s2.0-S0370269316000411&_mathId=si1.gif&_user=111111111&_pii=S0370269316000411&_rdoc=1&_issn=03702693&md5=fc1877ec9ab7d383146f53623195cc45" title="Click to view the MathML source">D0→e±μ∓ branching fraction is measured using the decay mode s2.0-S0370269316000411&_mathId=si28.gif&_user=111111111&_pii=S0370269316000411&_rdoc=1&_issn=03702693&md5=50acf2c2ba49be9507581c6d97f5c66b" title="Click to view the MathML source">D0→K−π+ as a normalization channel. No significant excess of s2.0-S0370269316000411&_mathId=si1.gif&_user=111111111&_pii=S0370269316000411&_rdoc=1&_issn=03702693&md5=fc1877ec9ab7d383146f53623195cc45" title="Click to view the MathML source">D0→e±μ∓ candidates over the expected background is seen, and a limit is set on the branching fraction, s2.0-S0370269316000411&_mathId=si8.gif&_user=111111111&_pii=S0370269316000411&_rdoc=1&_issn=03702693&md5=8fe2e966e026ab3053ca20b522e85073" title="Click to view the MathML source">B(D0→e±μ∓)<1.3×10−8, at 90% confidence level. This is an order of magnitude lower than the previous limit and it further constrains the parameter space in some leptoquark models and in supersymmetric models with R-parity violation.