If you're running T4 at design time (CustomTool: TextTemplatingFilePreprocessor), the template code gets executed as part of VisualStudio process. VisualStudio is loading devenv.exe.config and not your project config (you can check via AppDomain.CurrentDomain.SetupInformation.ConfigurationFile).
That's why you get null ref exception - 'localconnection' connection string is not in devenv.exe.config.
You can load your project config file using ConfigurationManager.OpenMappedExeConfiguration:
<#@ template debug="false" hostspecific="true" language="C#" #>
<#@ assembly name="System.Configuration" #>
<#@ import namespace="System.Configuration"#>
<#@ import namespace="System.IO" #>
<#
string configPath = Path.Combine(Host.ResolveAssemblyReference("$(ProjectDir)"), "App.config");
var configFileMap = new ExeConfigurationFileMap{ExeConfigFilename = configPath};
var config = ConfigurationManager.OpenMappedExeConfiguration(configFileMap, ConfigurationUserLevel.None);
string connectionString = config.ConnectionStrings.ConnectionStrings["localconnection"].ConnectionString;
WriteLine(connectionString);
#>
Note, it must be hostspecific="true" in order to use Host to resolve your project folder.