Context. We studied a sample of high proper motion, old and metal-rich dwarf stars, selected from the NLTT catalogue. The low pericentric distances and eccentric orbits of these solar neighbourhood stars indicate that they might have originated in the inner parts of the Galaxy. Aims. Chemical tagging can probe the formation history of stellar populations. To identify the origin of a sample of 71 very metal-rich dwarf stars, we derive the abundances of the neutron-capture elements Y, Ba, La, and Eu. Methods. The spectroscopic analysis is based on optical high-resolution échelle spectra obtained with the FEROS spectrograph at the ESO 1.52 m Telescope at La Silla, Chile. The abundances of Y, Ba, La, and Eu were derived through LTE analysis, employing the MARCS model atmospheres.Results. The abundances of Y, Ba, La, and Eu vs. Fe and Mg as the reference elements indicate similarities between our sample of old metal-rich dwarf stars and the thin disk. On the other hand, the abundance ratios using O as the reference element, as well as their kinematics, suggest that our sample is clearly distinct from the thin-disk stars. They could be old inner thin-disk stars, as suggested previously, or bulge stars. In either cases, they would have migrated from the inner parts of the Galaxy to the solar neighbourhood.