An examination of contemporary paintings and drawings of Maharaja Ranjit Singh done during his lifetime does not reveal any images of the Maharaja wearing a helmet. During his lifetime the Maharaja typically wore a turban and simple clothing.
The diminutive size of his person, and the comparative simplicity of his attire,—consisting of a turban, usually large only over the forehead, with the end hanging down the back, folded a la Sikh. (Vigne, 1840) 
He was dressed very plainly in green Cashmere turban, coat, and gloves, with single rows of large pearls down the breast, round his neck, and on his arms and legs, and a single string of very large diamonds round his arms. The Seikh turban, which so much disfigures the whole of this handsome race, does so particularly with him, and gives his countenance a low expression of cunning, which it would not probably otherwise have. (Fane, 1842) 
The Sikh pagri consists of a long narrow piece of linen, in which the hair is wrapped up; and it is so fastened either in the front or a little on one side, that one cannot see either end or knot. It lies down smooth on the head, one end hanging half way down the back. Ranjit Singh hides this end under his upper garment. (Hugel, 1845) 
The earliest images of Maharaja Ranjit Singh dating from 1810 and 1815-1820, done during the time period of his consolidation of his empire show the Maharaja wearing a simple cloth turban. The only piece of armour that the Maharaja ever wore on a regular basis and which is depicted in both of these early paintings is the dhal shield.
Ranjit Singh was quickly on the back of his steed, his shield at back, his like a common Sikh, and his face half hidden by the lower part of the turban which was wrapped over his chin. (Hugel, 1845) 
It is entirely open in front, and here, soon after dark, Runjeet retires to rest, sleeping in the open air, and guarded only by a few Sihk sipahis. His sword and shield are always laid by his pillow, and a horse saddled stands constantly ready in front of his tent. (Osborne, 1840) 
Maharaja Ranjit Singh kept tight control over both his empire as well as his royal court. Evidence reveals that not only did some members of his military wear helmets, but that members of the Sikh royal court also wore helmets. We have conclusive visual evidence such as the drawing of the Maharaja’s step-son Raja Sher Singh done by Osborne and Vigne between 1836 to 1838 showing Raja Sher Singh wearing a Indo-Persian style helmet as well as eyewitness accounts of helmets worn by members of the royal court in the Maharaja’s presence.
Ranjit Singh himself was seated in the European manner in a plain arm chair, and by him was Raja Hira Singh... Kushal Singh, the Jemidar, and Raja Sushet Singh, were the only state officers present. The last, a very fine distinguished man, wore a black and gold enamelled helmet with the visor open, and ornamented with three large black herons' feathers. (Hugel, 1845) 
During the important meeting between Maharaja Ranjit Singh and the British Governor General of India, Lord William Bentinck on the banks of the Sutlej river at Ropar in October 1831, Sohin Lal Suri, Maharaja Ranjit Singh’s official court chronicler recorded the fact that the important Sikh chieftains that accompanied the Maharaja to the meeting wore helmets:
The Maharaja at once crossed the river along with the above-mentioned Sahibs in the canopied boat. Then riding on horses, they all went to the camp of the Lal Sahib (the Governor General). All the chiefs and chieftans were decorated with four pieces (char-aina body armour plates), coats of mail and iron helmets and other armours, and they accompanied the stirrup of the Maharaja on horsebacks. 
A European eyewitness account of the same Ropar meeting provides further details indicating that while the chiefs wore Indo-Persian style helmets that day with prominent kalgi plumes the Maharaja himself wore a turban and not a helmet:
The chiefs appeard cap-a-pie, wearing round polished-steel helmets, surmounted with heron plumes, and burnished cuirasses, arm-pieces, and glaives, many neatly inliad with gold....On alighting, the Maharaja and his principal chiefs were conducted into the first of the state tents, where several of the officers of the escort and suite were introduced to his Highness : after this ceremony, a select number of his Sirdars accompanied him into an adjointing tent of equal size, connected with the first by a covered passage. Here his Highness being handed to a chair at the right of his Lordship, folded his legs up under him, in the attitude of Boodha seated upon his lotus throne. The Lion of Lahore is about fifty years of age, diminutive in stature, and emaciated in person...His forehead being completely covered by his yellow silk turban, it was impossible to ascertain its character. 
In his efforts to modernize the Khalsa army of the Sikh Empire, Maharaja Ranjit Singh clearly understood the benefits of armour including helmets to protect soldiers on the battlefield. It was under the stewardship of his French General Jean Francois Allard starting in 1822 that we see the first appearance of helmets among the cavalry of the Lahore Empire. Although we have conclusive proof of senior officers in the cavalry as well as high ranking members of the royal court wearing helmets, evidence that Maharaja Ranjit Singh himself ever having wore a helmet remains more elusive.
Perhaps the most important piece of circumstantail evidence to suggest that it is likely that the Maharaja did wear a helmet at some point during his reign comes from a rare set of armour from the Howard Ricketts Collection. The armour consists of a helmet, char-aina body armour plates, a coat of mail and arm guards. What is most significant about this armour is that the Indo-Persian style helmet as well as the breastplate and under arm plates all bear the inscription in gold lettering Devnagri script – ‘Maharaja Ranjit Singhji Bahadur’. This inscription directly connects this armour as having been the personal property of the Maharaja. It seems likely that having owned this full suit of armour including the Indo-Persian style helmet, that the Maharaja must have worn it at some time during his lifetime.
1. Personal Narrative of a Visit to Ghuzni, Kabul, and Afghanistan (London: 1840), 255-256
2. Henry Edward Fane, Five Years in India, Volume I (London: 1842), 132
3. Baron Charles Hugel, Translator Major T. B. Jervis, Travels in Kashmir and the Panjab (London: 1845), 380
4. Hugel, 305
5. W. G. Osborne, The Court and Camp of Runjeet Sing (London: 1840), 61
6. Hugel, 301
7. Sohan Lal Suri, Translator V.S. Suri, Umdat Ut-tawarikh, Daftar III (parts I-III) (Amritsar: Guru Nanak Dev University, 2002), 120
8. The United Service Journal and Naval and Military Magazine, Part II (London, 1832), 18-19