how to call different functions according to the template type parameter?

I'm using nlohmann::json to parse json string. I implement a util function GetValue to retrieve object fields.

template<typename T1, typename T2>
bool CheckType(T1& it, T2& val) { return false; }

template<typename T1>
bool CheckType(T1& it, bool& val) { return it->is_boolean(); }

template<typename T1>
bool CheckType(T1& it, std::string& val) { return it->is_string(); }

....

template<typename T>
bool GetValue(nlohmann::json obj, std::string key, T& value, std::string &err) {
    auto it = obj.find(key);
    if (it != obj.end()) {
        if (CheckType(it, val)) {
            value = it->get<T>();
            return true;
        } else {
            err = key + " type error";
        }
    } else {
        err = key + " not found";
    }
    return false;
}

The function CheckType looks ugly. What's the elegant way to do this?