We present Spitzer IRS spectra of four carbon stars located in the Galactic Halo and the thick disc. The spectra display typical features of carbon stars with SiC dust emission and C$_2$H$_2$ molecular absorption. Dust radiative transfer models and infrared colors enable us to determine the dust production rates for these stars whilst prior CO measurements yield expansion velocities and total mass-loss rates. The gas properties (low expansion velocities (around 7 km/s) and strong C$_2$H$_2$ molecular absorption bands) are consistent with the stars being metal-poor. However the dust content of these stars (strong SiC emission bands) is very similar to what is observed in metal-rich carbon stars. The strong SiC emission may indicate that the carbon stars derive from a metal-rich population, or that these AGB stars produce silicon. The origin of the halo carbon stars is not known. They may be extrinsinc halo stars belonging to the halo population, they may have been accreted from a satellite galaxy such as the Sagittarius Dwarf Spheroidal Galaxy, or they may be escapees from the galactic disk. If the stars are intrinsically metal-rich, an origin in the disc would be most likely. If an $alpha$-element enhancement can be confirmed, it would argue for an origin in the halo (which is known to be $alpha$-enhanced) or a Galactic satellite.
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