We are going find need and group what we find into Named Match Group =>  Captures. There will be two groups, one named Index which holds the A | B | C and then one named Data. 
The match will hold our data which will look like this:

From there we will join them into a dictionary:

Here is the code to do that magic:
string data =
@"""skip"" : {""A"":""ABCD123"",""B"":""ABCD1234"",""C"":""ABCD1235""}
""need"" : {""A"":""ZABCD123"",""B"":""ZABCD1234"",""C"":""ZABCD1235""}
""ignore"" : {""A"":""SABCD123"",""B"":""SABCD1234"",""C"":""SABCD1235""}";
string pattern = @"
\x22need\x22\s *:\s *{   # Find need
(                        # Beginning of Captures
   \x22                     #  Quote is \x22
   (?<Index>[^\x22] +)      # A into index.
   \x22\:\x22               # ':'
   (?<Data>[^\x22] +)       # 'Z...' Data
   \x22,?                   # ',(maybe)
)+                       # End of 1 to many Captures";
var mt = Regex.Match(data, 
                     pattern, 
                     RegexOptions.IgnorePatternWhitespace | RegexOptions.ExplicitCapture);
// Get the data capture into a List<string>.
var captureData = mt.Groups["Data"].Captures.OfType<Capture>()
                                            .Select(c => c.Value).ToList();
// Join the index capture data and project it into a dictionary.
var asDictionary = mt.Groups["Index"]
                     .Captures.OfType<Capture>()
                     .Select((cp, iIndex) => new KeyValuePair<string,string>
                                                 (cp.Value, captureData[iIndex]) )
                     .ToDictionary(kvp => kvp.Key, kvp => kvp.Value );