First of, who are "they?" Is it a company you are contracting for? Is it another department within a company you work for? Or perhaps a company you are working for as a temp through a staffing agency?
Second, is there any written contract (by you, the company, etc) ?
If there is no standing contract in place, and no understanding as far as intellectual property goes, I would say the source code is yours. But again - I would need to know more details to give a good answer. Often times temp agencies have people sign agreements that mention things like this, and if that is the case, "they" could have a legtimate claim to the source code. Please post more details, won't you?
UPDATE : So it sounds like you work for the company, but in another dept, eh? If that is the case, chances are the code belongs to the company. However, you may want to talk to your dept head, and see what they say about giving the source code to the other dept. As a general rule, if you work for a company, and develop code on their time, on their machines, they own the rights to the code - all of it. The only time you are immune from this is if you work as a contractor, with an explicit agreement that you retain ownership of the source code, and in special circumstances at a normal, hired position, where you have included a stipulation on your agreement to accept the position. This is very rare though, becuase it ties the company to you - and you alone - for the life of the program. Most companies want the rights to the source (for smaller apps) so they can maintain and modify as needed themselves. Hope this helps. If all else fails, contact the Compliance, or similar dept where you work - better safe than sorry.