Karen's relationship with Sandy is a purely positive one. They are both level-headed and intelligent characters with an appreciation for inventions, which is why they have had friendly interactions throughout the series.
In "Perfect Chemistry," the two meet and Sandy calls Karen beautiful. Karen is very happy about the compliment.
In "Salsa Imbecilicus," Karen and Sandy are the only residents of Bikini Bottom who were not turned into idiots by the stream from Plankton's sauce. They work together to create a university, which eventually returns everyone else to their normal intelligence. This episode reveals that Karen knows where Sandy lives and that her home is called a treedome, implying that she has visited Sandy.
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