You were arrested if you were taken to the station. Careless driving or reckless driving?
You should answer that you were arrested on suspicion of DUI and that the ticket issued was for careless driving. That is, tell the truth.
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If you are applying for a law enforcement agency, you should certainly mention that you were arrested on suspicion of DUI but tested negative and were given a ticket for careless driving.
They will do a very thorough background check and I am certain your arrest will come up. So if you don't mention it, it will look bad.
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The application requires full disclosure I believe. You were "arrested" but your abstact will only show the final charge (not even the careless if the dispostion was less). If the question is if you were ever arrested you need to say yes. If it is "arrested for a serious charge or crime" you can say no but you have that overriding disclosure requirement.
An arrest not resulting in conviction will not keep you from a law enforcement job. The appearance that you are lying or hiding something will. It is a good idea to run background checks on yourself through the State Police and the MVC to determine what exactly is on your background before completing applications.