Can an independent vote in both the Democratic and Republican primaries?

So, I was interested in doing this myself. I have an answer but I can only say for sure that it's the case in New Jersey. I emailed my county clerk:

"I am already a registered voter, but not affiliated with any party. My standpoints are in line with different parties on different issues; I would like to know if it is possible to have more than one party affiliation at the same time. If this is not permitted, I am curious as to whether your office can inform me of the specific law that prevents this."

Here is the response:

"The statue on such matters is NJSA 19:23-45. An individual may have only one party affiliation at a time.

An individual can change party affiliations and can also now change from a particular party back to being unaffiliated.A unaffiliated voter can declare party affiliation at the polls on primary election day."

Thus, it looks like the answer, for New Jersey at least, is No.

However, there are some states that do not give their voters the option of registering with a party. See the related links for a story about this, which brought it to my attention. I don't know if you're prevented from voting in multiple primaries in these states, but regardless of which one you choose, they are open to everyone.

My suggestion is that anyone coming across this suggestion whose state is not included here should email their county clerk and ask this question (you can use my email as a template) and post the answer here.