How can we check Perl input-output handle

A few years back I wrote FileHandle::Fmode. It hasn't been updated in the last 7 years, but I think it still functions correctly and, IIUC, it provides the sort of info you're seeking.
Here's an excerpt from the POD that documents the functions that it provides:

 $bool = is_FH($fh);
 $bool = is_FH(\*FH);
  This is just a (more intuitively named) alias for is_arg_ok().
  Returns 1 if its argument is an open filehandle.
  Returns 0 if its argument is something other than an open filehandle
+.

 $bool = is_arg_ok($fh);
 $bool = is_arg_ok(\*FH);
  Returns 1 if its argument is an open filehandle.
  Returns 0 if its argument is something other than an open filehandle
+.

 Arguments to the following functions  must be open filehandles. If
 any of those functions receive an argument that is not an open
 filehandle then the function dies with an appropriate error message.
 To ensure that your script won't suffer such a death, you could first
 check by passing the argument to is_FH(). Or you could wrap the
 function call in an eval{} block.

Note that it may be possible that a filehandle opened for writing may
become unwritable - if (eg) the disk becomes full. I don't know how
the below functions would be affected by such an event. I suspect
that they would be unaware of the change ... but I haven't actually
checked.


 $bool = is_R($fh);
 $bool = is_R(\*FH);
  Returns true if the filehandle is readable.
  Else returns false.

 $bool = is_W($fh);
 $bool = is_W(\*FH);
  Returns true if the filehandle is writable.
  Else returns false.

 $bool = is_RO($fh);
 $bool = is_RO(\*FH);
  Returns true if the filehandle is readable but not writable.
  Else returns false.

 $bool = is_WO($fh);
 $bool = is_WO(\*FH);
  Returns true if the filehandle is writable but not readable.
  Else returns false.

 $bool = is_RW($fh);
 $bool = is_RW(\*FH);
  Returns true if the filehandle is both readable and writable.
  Else returns false.

 $bool = is_A($fh);
 $bool = is_A(\*FH);

  Returns true if the filehandle was opened for appending.
  Else returns false.
  Not currently implemented on Win32 with pre-5.6.1 versions of perl (
+and
  dies with appropriate error message if called on such a platform).
[download]

Cheers,
Rob