SendingToLogicApp.cs

var client = new HttpClient();

var request = new HttpRequestMessage
{
    RequestUri = new Uri(PostTweetUrl),
    Method = HttpMethod.Post
};

var json = $"{{\"key\":\"{hash}\",\"twittername\":\"@@LBugnion\"}}";

request.Content = new StringContent(json, Encoding.UTF8, "application/json");

await client.SendAsync(request);