Are you on friendly/cordial terms with the super? Is he basically a nice guy? I would be willing to bet that he is, and that he doesn't like the idea that a little girl is frightened of him any more than you like it. Maybe you can talk to him about it when your daughter isn't around, and then enlist his help and arrange a time when you and your daughter can go "meet" him and you can properly introduce her to him and show her that he's a nice guy who won't hurt her. If he feels comfortable talking to her in a friendly way when you are there, or engaging you in friendly conversation in front of her, that might help too. I think she needs to see that he's just a nice, ordinary man, that he didn't mean to startle her or scare her -- and if you model that you aren't afraid of him, and you make it a point to say hi to him when you see him, and otherwise are on friendly terms with him, and if he might be willing to help you out with this by responding in kind, she should eventually see that he is not some kind of scary monster, but just a nice man who works/lives in your building.
I am appalled, frankly, that people are jumping to conclusions that this man is some kind of molester or something just because your daughter is scared of him -- I would rather see the good in people than jump to conclusions that a three year old has a "reason" to fear him. You didn't say that she was alone when he startled her -- and at her age, I would assume she wasn't, but that you or another adult were with her -- and I'm sure he didn't do that on purpose, either. Children of that age are not able to "reason" why they are scared of something or someone. The amount of paranoia among some of the other respondants to this question, and the immediate leap to "he probably touched her inappropriately" is utterly, utterly insane to me...no, I don't think he did anything inappropriate to the child, I just think she's developed a fear based upon remembering being startled accidentally. Not everyone is some kind of pervert, and it's not fair to brand this man by saying that a not yet three year old child has the rational sense to be scared of him because he is or might be! I'm all for keeping our kids safe, but this does not sound to me like anything more than a simple case of memory linked to fear that can be overcome.
Best of luck to you with this.
S. :)