Either Object.class or Object.type should do what you need.
Also, the two methods Object.is_a? and Object.instance_of? can be used. However, they are not 100% identical. The statement obj.instance_of?(myClass) will return true only if object obj was created as an object of type myClass. Using obj.is_a?(myClass) will return true if the object obj is of class myClass, is of a class that has inherited from myClass, or has the module myClass included in it.
For example:
x = 1
x.class => Fixnum
x.instance_of? Integer => false
x.instance_of? Numeric => false
x.instance_of? Fixnum => true
x.is_a? Integer => true
x.is_a? Numeric => true
x.is_a? Fixnum => true
Since your C# method requires a very specific data type, I would recommend using Object.instance_of?.