10 December 1893
If by "double spirit" you mean a spirit with the the appearance, memories, and personality of someone who was living and is now dead: that's just a spirit and the adjective is unnecessary. If by "doppelgänger" you mean a corporeal being with the appearance of a now-deceased person: no, those do not exist. If you in fact meant neither of those things, please clarify your inquiry.
You may also consider whether the interaction in question could have been caused by a boggart (which is the purview of this division) or by someone using polyjuice potion (which is not).
F. Greengrass
Spirit Division, Ministry of Magic
Spirit Division, Ministry of Magic
Set by Lady!