I think that this is not possible because Int32 has 1 bit sign and have 31 bit of numeric information and Int16 has 1 bit sign and 15 bit of numeric information
This should work:
int original = ...;
byte[] bytes = BitConverter.GetBytes(original);
short firstHalf = BitConverter.ToInt16(bytes, 0);
short secondHalf = BitConverter.ToInt16(bytes, 2);
EDIT:
tested with 0x7FFFFFFF, it works
byte[] recbytes = new byte[4];
recbytes[0] = BitConverter.GetBytes(firstHalf)[0];
recbytes[1] = BitConverter.GetBytes(firstHalf)[1];
recbytes[2] = BitConverter.GetBytes(secondHalf)[0];
recbytes[3] = BitConverter.GetBytes(secondHalf)[1];
int reconstituted = BitConverter.ToInt32(recbytes, 0);