I do not see any reason to limit a presidential candidate who has been arrested, there is no reason to take them off the ballot. If this were to happen, it would be well documented, as well as be picked up by the media and widely covered. This in turn would change people's mind about said candidate rather they were arrested for a good reason or not.
Yes, a presidential candidate who is arrested should be allowed on the ballot. Even if they commit wrongdoings, they still declared their candidacy for president, so they have a right to be on the ballot. They probably will not even win anyway, because many people do not want a criminal running their country.
We probably should not be voting for most of the candidates on the presidential ballot, but that does not mean they shouldn't be there. An arrest is not a conviction, and so it would be easy to just have police arrest those whom a certain faction did not want to run.
If people who were arrested were legally barred from being president then what kind of message are we sending to the people of the US? People are falsely arrested, or arrested for minor offenses (traffic violations etc) with fair frequency, but, more, if we bar those arrested from office then we're saying that rehabilitation is impossible, and that one mistake is the end of the world.
A presidential candidate who is arrested should be allowed on the ballot. We should not hold them accountable for something that happened in the past but what they do in office is more important than anything else. What a politician does in their personal time should be their own business but with social media that is not the case anymore.