Most of the gaseous molecules that are detected in cometary atmospheres are produced through sublimation of nucleus ices. Distributed sources may also occur, that is, production within the coma, from the solid component of dust particles that are ejected from the nucleus. Glycine, the simplest amino acid, was observed episodically in the atmosphere of comet 67P/Churyumov-Gerasimenko (67P) by the ROSINA mass spectrometer on board the Rosetta probe. A series of measurements on 28 March 2015 revealed a distributed density profile at between 14 and 26 km away from the nucleus. We here present and discuss three study cases: (i) glycine emitted directly and only from the nucleus, (ii) glycine emitted from the sublimation of solid-state glycine on the dust particles that are ejected from the nucleus, and (iii) glycine molecules embedded in water ice that are emitted from the sublimation of this ice from the dust particles that are ejected from the nucleus. A numerical model was developed to calculate the abundance of glycine in the atmosphere of comet 67P as a function of the distance from the nucleus, and to derive its initial abundance in the lifted dust particles. We show that a good fit to the observations corresponds to a distributed source of glycine that is embedded in sublimating water ice from dust particles that are ejected from the nucleus (iii). The few hundred ppb of glycine embedded in water ice on dust particles (nominally 170 ppb by mass) agree well with the observed distribution.