how to make a subclass constructor to act exatly like its superclass?

Richard's answer is correct, but it is worth mentioning how to go about it.

For example, the string class has a constructor string(char *str).
Then you would define your class with the same constructor, and call the base class constructor as follows:

class CText : public string
{
    CText(char *str) : string(str) { } //This calls the base class constructor
    //more constructors and other functions
}

If you can rely on C++11, a simple way can be

class CText: public string
{
public:
    template<class... T>
    CText(T&&... t) :string(forward<T>(t)...) 
    {}

    ...
};

Essentially the constructor is based on a varadic template (taking form 0 to whatever number of argument of whatever types) that are taking in term of r-value reference (think to it as a relaxed const&, that can also take and modify temporary values) and forwarded (in C++0x a && becomes a & when passed as argument: forward, just casts it back to &&) one-to-one to the base class.

As a result, until there is a constructor in string that takes certain parameters, They can be taken by the superclass as well.

You need to define like this,

CText(string str)
{
}