If the charges WERE dismissed, the issue is whether they were dismissed with prejudice or without. If the former, they cannot be brought again without production of new evidence not available when the charges were first brought.
If the charges were not dismissed with prejudice; merely dropped, they could be brought again.
The simple answer is yes. The same charges can be brought against you again after they were dismissed or reduced, unless they were dismissed with prejudice (which is very rare), or they were dropped after jeopardy had attached (in other words, if they dropped the charges after the trial had already begun: after witnesses were sworn in a bench trial, or after the jury was impaneled at a jury trial).
"Dropped" can mean amended to a lesser charge, or dismissed altogether. You can be charged with more crimes after a dismissal or an amended of the original crimes. Also, if certain charges were dismissed without prejudice, the prosecution can re-apply for issuance of another complaint for the crime(s) that was dismissed. If the original crime was amended to a lesser charge, it is unlikely that that charge would be re-amended back up to the original charge and if the DA attempts to do so your attorney should object to it.