Can HUF Issue form 15 G

Yes. HUF can issue Form 15G. If you go through Form No. 15G, it reads as under: "Declaration under sub sec (1) and (1A) of section 197A to be made by an Individual OR A PERSON (NOT BEING A COMPANY OR FIRM) claiming certain receipts............". Thus an HUF is also covered in the above.

Regarding your grand mother, if she has no taxable income, i.e. if her tax liability is NIL, she can definitely issue Form No. 15H and that will be the wise thing to do instead of going through the procedure of claiming refund later on.

 Thank you Sandeep....

The only thing im ltl confused is that it reads as form 15G can be given by person who doesnot have any other Income (xcept Interest) Since my HUF has nominal income from Shares (though not taxable) 

The reason im  clarifing is that as i understand the IT law for wrongly given forms are pretty stirct. So double checking every word of the form....