Is there a mountain biking or hiking organization in your area? If there is, they MAY be working with Parks already on that. We ran into a situation locally where trails in a park were maintained by a hiking group, except for a series of trails that were built by mountain bikers that had jumps and G-outs and stuff like that on them that hikers didn't like. We made contact with the county Parks office, and they said, roughly:
We're happy to have you maintain the trails if you want to. We like them, but we didn't build them, and we don't maintain them, we don't even look at them, but they're on our map. If you want to work on the trails contact this hiking group, because they've been working on the trails as well.
So we got in touch with the hiking group and found out they were getting to be a smaller group and short on man power, so as an MTB club, we took over the trails, but still get help on our workdays from hikers in this group. So yes, step one, get permission - always get permission first. Otherwise, as someone else pointed out, you could cause problems for you and everyone else - and it's a terrible thing to put all the work into a trail that it can take, and find out all you did was cause problems.
Once you have permission, make sure you aren't stepping on anyone's toes. People and groups can get possessive of trails, and not just because they built them, but because they know they have permission to work on them, so officially what's done to the trails seems to have been done by that person or group. If someone stupid is done (a big ramp built using a shipping pallet, for instance) it may reflect badly on the group or person, even though they didn't do it. Plus, if you have a group doing work already, they may be willing to pitch in and help you, especially if you pitch in and help them.