What type of paint is it?...water based?...cover with a boiling hot rag and leave for 15 mins...the heat will soften the paint...thus avoiding to much scraping..
Oil based...go with uncle Nesters solution..it shoulnt do any harm..maybe try a little area first our of site just in case there is a reaction.
If it's an emulsion paint, then you can just clean it off the sink with any strong solvent, like acetone, lacquer thinner, xylene, MEK. Even most alcohols will dissolve emulsion paints. The rubbing alcohol in your cabinet will do it (as will nail polish remover).
You'll need a paint stripper to take it off if it's an oil based paint. Either that or a heat gun.
If it's an epoxy, I try a heat gun on it before I gave up.
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