So long as you didn't plea guilty or no contest then the charges have been dismissed and you can honestly say no to being convicted of a felony. Of course if the question is, have you been arrested for a felony that may be a different answer. Until you get the charge sealed or expunged, the arrest (but not conviction since you were not convicted) will continue to show up on background checks. I strongly suggest you look into getting the charge expunged so that it doesn't show up on background checks. I practice in Tampa if you wish to give me a call at my website number below. Also, check my link on sealing on expunging.
A letter of release generally indicates that charges were never filed. After charges are filed, if the State were to drop the case, they would file a notice of nolle prosequi. Therefore, if this is your only concern, you have never been charged with a felony. As Mr. Epifanio indicated though, the arrest will continue to show up on background checks. Getting it expunged is an important step to clearing the arrest. Once the expungement is granted, an attorney can forward copies of the order to various background check companies to have it removed from their database as well.
Good luck with the background check and if you would like assistance going through the expungement process, feel free to give me a call.